Cosmogenesis

As already pointed out in a previous Golden Oldie devoted to the Lemaitre’s short note of 1931 which can be considered as the true “Charter” of the modern big bang theory [1], although the Belgian scientist was primarily a remarkable mathematician and a theoretical physicist, he stayed closely related to astronomy all his life and always felt the absolute need for confronting the observational data and the general relativity theory. This basic fact explains why as soon as 1927, while still a beginner in cosmology, he was the first one to be able to understand the recent observations on the recession velocities of galaxies as a natural consequence of dynamical cosmological solutions of Einstein’s field equations.1 Before examining in detail the contents of his outstanding article, let us summarize the road which, in the few preceding years, led the young Lemaitre to the expanding universe (see e.g. [6]). In 1923, the same year as he was ordained as a priest, Georges Lemaitre obtained a 3-year fellowship from the Belgian government, enabling him to study abroad.

@article{doi101093mnras915483,
    author = "Lematre, A. G.",
    title = "A Homogeneous Universe of Constant Mass and Increasing Radius accounting for the Radial Velocity of Extra-galactic Nebulae",
    year = "1931",
    journal = "Monthly Notices of the Royal Astronomical Society",
    abstract = "As already pointed out in a previous Golden Oldie devoted to the Lemaitre’s short note of 1931 which can be considered as the true “Charter” of the modern big bang theory [1], although the Belgian scientist was primarily a remarkable mathematician and a theoretical physicist, he stayed closely related to astronomy all his life and always felt the absolute need for confronting the observational data and the general relativity theory. This basic fact explains why as soon as 1927, while still a beginner in cosmology, he was the first one to be able to understand the recent observations on the recession velocities of galaxies as a natural consequence of dynamical cosmological solutions of Einstein’s field equations.1 Before examining in detail the contents of his outstanding article, let us summarize the road which, in the few preceding years, led the young Lemaitre to the expanding universe (see e.g. [6]). In 1923, the same year as he was ordained as a priest, Georges Lemaitre obtained a 3-year fellowship from the Belgian government, enabling him to study abroad.",
    url = "https://doi.org/10.1093/mnras/91.5.483",
    doi = "10.1093/mnras/91.5.483",
    openalex = "W2129362056",
    references = "doi101007bf01332580"
}

@article{doi101038246396a0,
    author = "Tryon, E. P.",
    title = "Is the Universe a Vacuum Fluctuation?",
    year = "1973",
    journal = "Nature",
    url = "https://doi.org/10.1038/246396a0",
    doi = "10.1038/246396a0",
    openalex = "W2073716472",
    references = "doi1010160370157372900099, doi10106313021960, doi101103physrevb7326, doi101103physrevd7326, doi101103physrevlett281541"
}

@misc{hill1976how3,
    author = "Hill, H",
    title = "How Did It All Begin?",
    year = "1976",
    howpublished = "Plainfield, New Jersey, Logos International",
    note = "talkorigins\_source = {true}; raw\_reference = {Hill, H., 1976, How Did It All Begin?: Plainfield, New Jersey, Logos International.}"
}

@article{doi1010160003491678901768,
    author = "Brout, R. and Englert, F. and Gunzig, E.",
    title = "The creation of the universe as a quantum phenomenon",
    year = "1978",
    journal = "Annals of Physics",
    url = "https://doi.org/10.1016/0003-4916(78)90176-8",
    doi = "10.1016/0003-4916(78)90176-8",
    openalex = "W2039108312",
    references = "doi1010160003491670903945, doi101038246396a0, doi10106313022395, doi101093mnras1166662, doi101103physrev1831057, doi101103physrevd10275, doi101103physrevd84231, doi101103physrevlett378, doi104159harvard9780674734487"
}

@misc{slusher1978the5,
    author = "Slusher, H. S",
    title = "The origin of the universe",
    year = "1978",
    howpublished = "an examination of the big-bang and steady-state cosmogenies: ICR Technical Monograph, v. 8; Institute for Creation Research, 50 pp",
    note = "talkorigins\_source = {true}; raw\_reference = {Slusher, H. S., 1978, The origin of the universe: an examination of the big-bang and steady-state cosmogenies: ICR Technical Monograph, v. 8; Institute for Creation Research, 50 pp.}"
}

The standard model of hot big-bang cosmology requires initial conditions which are problematic in two ways: (1) The early universe is assumed to be highly homogeneous, in spite of the fact that separated regions were causally disconnected (horizon problem); and (2) the initial value of the Hubble constant must be fine tuned to extraordinary accuracy to produce a universe as flat (i.e., near critical mass density) as the one we see today (flatness problem). These problems would disappear if, in its early history, the universe supercooled to temperatures 28 or more orders of magnitude below the critical temperature for some phase transition. A huge expansion factor would then result from a period of exponential growth, and the entropy of the universe would be multiplied by a huge factor when the latent heat is released. Such a scenario is completely natural in the context of grand unified models of elementary-particle interactions. In such models, the supercooling is also relevant to the problem of monopole suppression. Unfortunately, the scenario seems to lead to some unacceptable consequences, so modifications must be sought.

@article{doi101103physrevd23347,
    author = "Guth, Alan H.",
    title = "Inflationary universe: A possible solution to the horizon and flatness problems",
    year = "1981",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
    abstract = "The standard model of hot big-bang cosmology requires initial conditions which are problematic in two ways: (1) The early universe is assumed to be highly homogeneous, in spite of the fact that separated regions were causally disconnected (horizon problem); and (2) the initial value of the Hubble constant must be fine tuned to extraordinary accuracy to produce a universe as flat (i.e., near critical mass density) as the one we see today (flatness problem). These problems would disappear if, in its early history, the universe supercooled to temperatures 28 or more orders of magnitude below the critical temperature for some phase transition. A huge expansion factor would then result from a period of exponential growth, and the entropy of the universe would be multiplied by a huge factor when the latent heat is released. Such a scenario is completely natural in the context of grand unified models of elementary-particle interactions. In such models, the supercooling is also relevant to the problem of monopole suppression. Unfortunately, the scenario seems to lead to some unacceptable consequences, so modifications must be sought.",
    url = "https://doi.org/10.1103/physrevd.23.347",
    doi = "10.1103/physrevd.23.347",
    openalex = "W2134251287",
    references = "doi1010160003491675902110, doi1010160016003274900623, doi1010160550321374904866, doi1010880305447098029, doi101103physrevd152929, doi101103physrevd161762, doi101103physrevd71888, doi101103physrevd93320, doi101103physrevlett32438, doi101103revmodphys51591"
}

@book{doi1015159780691206714,
    author = "Peebles, P. J. E.",
    title = "The Large-Scale Structure of the Universe",
    year = "1981",
    booktitle = "Princeton University Press eBooks",
    url = "https://doi.org/10.1515/9780691206714",
    doi = "10.1515/9780691206714",
    openalex = "W4292930832"
}

@misc{vandenbergh1981size6,
    author = "Van den Bergh, S",
    title = "Size and age of the universe",
    year = "1981",
    howpublished = "Science, v. 213, p. 825- 830",
    note = "talkorigins\_source = {true}; raw\_reference = {Van den Bergh, S., 1981, Size and age of the universe: Science, v. 213, p. 825- 830.}"
}

@article{doi1010160370269382903732,
    author = "Hawking, S. W.",
    title = "The development of irregularities in a single bubble inflationary universe",
    year = "1982",
    journal = "Physics Letters B",
    url = "https://doi.org/10.1016/0370-2693(82)90373-2",
    doi = "10.1016/0370-2693(82)90373-2",
    openalex = "W1987010236"
}

@article{doi101016037026938290541x,
    author = "Starobinsky, Alexei A.",
    title = "Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations",
    year = "1982",
    journal = "Physics Letters B",
    url = "https://doi.org/10.1016/0370-2693(82)90541-x",
    doi = "10.1016/0370-2693(82)90541-x",
    openalex = "W2035784745",
    references = "doi101016c20090146081, doi10106313050989"
}

@article{doi1010160370269382909467,
    author = "Hawking, S. W. and Moss, Ian G.",
    title = "Supercooled phase transitions in the very early universe",
    year = "1982",
    journal = "Physics Letters B",
    url = "https://doi.org/10.1016/0370-2693(82)90946-7",
    doi = "10.1016/0370-2693(82)90946-7",
    openalex = "W1981083641"
}

@article{doi1010160370269382912199,
    author = "Linde, Andrei",
    title = "A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems",
    year = "1982",
    journal = "Physics Letters B",
    url = "https://doi.org/10.1016/0370-2693(82)91219-9",
    doi = "10.1016/0370-2693(82)91219-9",
    openalex = "W1973861971"
}

We present a nonsingular model of cosmogenesis in which the Universe arises as a result of quantum-mechanical barrier penetration. The Universe is described throughout its evolution by a Friedmann-Robertson-Walker (FRW) metric, and the matter distribution by a perfect fluid, whose equation of state is chosen so as to allow the tunneling to occur. Cosmic evolution proceeds in three stages; an initial static spacetime configuration tunnels into a "fireball" state in which particle creation occurs. As the fireball expands, particle creation ends, and the Universe enters the "post-big-bang" epoch of adiabatic expansion. We find that within the context of the FRW ansatz, only a spatially closed universe may originate in this manner. Implications of this creation scheme and possible generalizations are discussed. As a by-product of this investigation we find that the evolution of the Universe is described by a Gell-Mann---Low equation with the $\ensuremath{\beta}$ function specified by the equation of state.

@article{doi101103physrevd252065,
    author = "Atkatz, David and Pagels, Heinz",
    title = "Origin of the Universe as a quantum tunneling event",
    year = "1982",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
    abstract = {We present a nonsingular model of cosmogenesis in which the Universe arises as a result of quantum-mechanical barrier penetration. The Universe is described throughout its evolution by a Friedmann-Robertson-Walker (FRW) metric, and the matter distribution by a perfect fluid, whose equation of state is chosen so as to allow the tunneling to occur. Cosmic evolution proceeds in three stages; an initial static spacetime configuration tunnels into a "fireball" state in which particle creation occurs. As the fireball expands, particle creation ends, and the Universe enters the "post-big-bang" epoch of adiabatic expansion. We find that within the context of the FRW ansatz, only a spatially closed universe may originate in this manner. Implications of this creation scheme and possible generalizations are discussed. As a by-product of this investigation we find that the evolution of the Universe is described by a Gell-Mann---Low equation with the $\ensuremath{\beta}$ function specified by the equation of state.},
    url = "https://doi.org/10.1103/physrevd.25.2065",
    doi = "10.1103/physrevd.25.2065",
    openalex = "W2147104319",
    references = "doi101007bf01208277, doi101007bf01649434, doi1010160003491678901768, doi1010160550321381900213, doi101038246396a0, doi10108800319112314029, doi101103physrev1831057, doi101103physrev951300, doi101103physrevd152752, doi101103physrevd21541"
}

The spectrum of density perturbations is calculated in the new-inflationary-universe scenario. The main source is the quantum fluctuations of the Higgs field, which lead to fluctuations in the time at which the false vacuum energy is released. The value of $\frac{\ensuremath{\delta}\ensuremath{\rho}}{\ensuremath{\rho}}$ on any given length scale $l$, at the time when the Hubble radius $\ensuremath{\gg}l$, is estimated. This quantity is nearly scale invariant (as desired), but is unfortunately about ${10}^{5}$ times too large.

@article{doi101103physrevlett491110,
    author = "Guth, Alan H. and Pi, So-Young",
    title = "Fluctuations in the New Inflationary Universe",
    year = "1982",
    journal = "Physical Review Letters",
    abstract = "The spectrum of density perturbations is calculated in the new-inflationary-universe scenario. The main source is the quantum fluctuations of the Higgs field, which lead to fluctuations in the time at which the false vacuum energy is released. The value of $\frac{\ensuremath{\delta}\ensuremath{\rho}}{\ensuremath{\rho}}$ on any given length scale $l$, at the time when the Hubble radius $\ensuremath{\gg}l$, is estimated. This quantity is nearly scale invariant (as desired), but is unfortunately about ${10}^{5}$ times too large.",
    url = "https://doi.org/10.1103/physrevlett.49.1110",
    doi = "10.1103/physrevlett.49.1110",
    openalex = "W2164459358"
}

The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and $\ensuremath{\Lambda}>0$. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier to a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.

@article{doi101103physrevd282960,
    author = "Hartle, James B. and Hawking, S. W.",
    title = "Wave function of the Universe",
    year = "1983",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
    abstract = {The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and $\ensuremath{\Lambda}>0$. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier to a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.},
    url = "https://doi.org/10.1103/physrevd.28.2960",
    doi = "10.1103/physrevd.28.2960",
    openalex = "W2147762346",
    references = "doi101007354012291524, doi101007bf01626516, doi1010160370269382908668, doi101016055032137890161x, doi101049sqj19660063, doi101103physrev1601113, doi101103physrevd152929, doi101103physrevd272848, doi101103physrevlett281082, doi101103revmodphys20367"
}

@article{doi1010160550321384900932,
    author = "Hawking, S. W.",
    title = "The quantum state of the universe",
    year = "1984",
    journal = "Nuclear Physics B",
    url = "https://doi.org/10.1016/0550-3213(84)90093-2",
    doi = "10.1016/0550-3213(84)90093-2",
    openalex = "W2011866921"
}

According to the inflationary Universe scenario the Universe in the very early stages of its evolution was exponentially expanding in the unstable vacuumlike state. At the end of the exponential expansions (inflation) the energy of the unstable vacuum (of a classical scalar field) transforms into the energy of hot dense matter, and the subsequent evolution of the Universe is described by the usual hot Universe theory. Recently it was realised that the exponential expansion during the very early stages of evolution of the Universe naturally occurs in a wide class of realistic theories of elementary particles. The inflationary Universe scenario makes it possible to obtain a simple solution to many long-standing cosmological problems and leads to a crucial modification of the standard point of view of the large-scale structure of the Universe.

@article{doi10108800344885478002,
    author = "Linde, Andrei",
    title = "The inflationary Universe",
    year = "1984",
    journal = "Reports on Progress in Physics",
    abstract = "According to the inflationary Universe scenario the Universe in the very early stages of its evolution was exponentially expanding in the unstable vacuumlike state. At the end of the exponential expansions (inflation) the energy of the unstable vacuum (of a classical scalar field) transforms into the energy of hot dense matter, and the subsequent evolution of the Universe is described by the usual hot Universe theory. Recently it was realised that the exponential expansion during the very early stages of evolution of the Universe naturally occurs in a wide class of realistic theories of elementary particles. The inflationary Universe scenario makes it possible to obtain a simple solution to many long-standing cosmological problems and leads to a crucial modification of the standard point of view of the large-scale structure of the Universe.",
    url = "https://doi.org/10.1088/0034-4885/47/8/002",
    doi = "10.1088/0034-4885/47/8/002",
    openalex = "W2034898285",
    references = "doi1010160003491678901768, doi101038246396a0"
}

It is assumed that the Universe is in the quantum state defined by a path integral over compact four-metrics. This can be regarded as a boundary condition for the wave function of the Universe on superspace, the space of all three-metrics and matter field configurations on a three-surface. We extend previous work on finite-dimensional approximations to superspace to the full infinite-dimensional space. We treat the two homogeneous and isotropic degrees of freedom exactly and the others to second order. We justify this approximation by showing that the inhomogeneous or anisotropic modes start off in their ground state. We derive time-dependent Schr\"odinger equations for each mode. The modes remain in their ground state until their wavelength exceeds the horizon size in the period of exponential expansion. The ground-state fluctuations are then amplified by the subsequent expansion and the modes reenter the horizon in the matter- or radiation-dominated era in a highly excited state. We obtain a scale-free spectrum of density perturbations which could account for the origin of galaxies and all other structure in the Universe. The fluctuations would be compatible with observations of the microwave background if the mass of the scalar field that drives the inflation is ${10}^{14}$ GeV or less.

@article{doi101103physrevd311777,
    author = "Halliwell, J. J. and Hawking, S. W.",
    title = "Origin of structure in the Universe",
    year = "1985",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
    abstract = {It is assumed that the Universe is in the quantum state defined by a path integral over compact four-metrics. This can be regarded as a boundary condition for the wave function of the Universe on superspace, the space of all three-metrics and matter field configurations on a three-surface. We extend previous work on finite-dimensional approximations to superspace to the full infinite-dimensional space. We treat the two homogeneous and isotropic degrees of freedom exactly and the others to second order. We justify this approximation by showing that the inhomogeneous or anisotropic modes start off in their ground state. We derive time-dependent Schr\"odinger equations for each mode. The modes remain in their ground state until their wavelength exceeds the horizon size in the period of exponential expansion. The ground-state fluctuations are then amplified by the subsequent expansion and the modes reenter the horizon in the matter- or radiation-dominated era in a highly excited state. We obtain a scale-free spectrum of density perturbations which could account for the origin of galaxies and all other structure in the Universe. The fluctuations would be compatible with observations of the microwave background if the mass of the scalar field that drives the inflation is ${10}^{14}$ GeV or less.},
    url = "https://doi.org/10.1103/physrevd.31.1777",
    doi = "10.1103/physrevd.31.1777",
    openalex = "W2017483000"
}

@book{cohen1988in1,
    author = "Cohen, M",
    title = "In Darkness Born",
    year = "1988",
    publisher = "The Story of Star Formation: Cambridge, Cambridge University Press",
    note = "talkorigins\_source = {true}; raw\_reference = {Cohen, M., 1988, In Darkness Born: The Story of Star Formation: Cambridge, Cambridge University Press.}"
}

@incollection{doi10100735401645296,
    author = "Starobinsky, Alexei A.",
    title = "Stochastic de sitter (inflationary) stage in the early universe",
    year = "1988",
    booktitle = "Lecture notes in physics",
    url = "https://doi.org/10.1007/3-540-16452-9\_6",
    doi = "10.1007/3-540-16452-9\_6",
    openalex = "W1593303744",
    references = "doi101038246396a0"
}

There is sufficient evidence at present to justify the belief that the universe began to exist without being caused to do so. This evidence includes the Hawking-Penrose singularity theorems that are based on Einstein's General Theory of Relativity, and the recently introduced Quantum Cosmological Models of the early universe. The singularity theorems lead to an explication of the beginning of the universe that involves the notion of a Big Bang singularity, and the Quantum Cosmological Models represent the beginning largely in terms of the notion of a vacuum fluctuation. Theories that represent the universe as infinitely old or as caused to begin are shown to be at odds with or at least unsupported by these and other current cosmological notions.

@article{doi101086289415,
    author = "Smith, Quentin",
    title = "The Uncaused Beginning of the Universe",
    year = "1988",
    journal = "Philosophy of Science",
    abstract = "There is sufficient evidence at present to justify the belief that the universe began to exist without being caused to do so. This evidence includes the Hawking-Penrose singularity theorems that are based on Einstein's General Theory of Relativity, and the recently introduced Quantum Cosmological Models of the early universe. The singularity theorems lead to an explication of the beginning of the universe that involves the notion of a Big Bang singularity, and the Quantum Cosmological Models represent the beginning largely in terms of the notion of a vacuum fluctuation. Theories that represent the universe as infinitely old or as caused to begin are shown to be at odds with or at least unsupported by these and other current cosmological notions.",
    url = "https://doi.org/10.1086/289415",
    doi = "10.1086/289415",
    openalex = "W2066505440",
    references = "doi1010160370269382908668, doi101017cbo9780511524646, doi101038246396a0, doi101073pnas153168, doi10108000018736300101283, doi101086148307, doi101098rspa19700021, doi101103physrevd142460, doi101103physrevd252065, doi101103physrevlett1457, openalexw3021036590"
}

@book{guth1988the2,
    author = "Guth, A. H",
    title = "The Birth of the Cosmos, in Osterbrock, D. E., and Raven, P. H., eds., Origins and Extinctions",
    year = "1988",
    publisher = "New Haven, Connecticut, Yale University Press, p. 1-41",
    note = "talkorigins\_source = {true}; raw\_reference = {Guth, A. H., 1988, The Birth of the Cosmos, in Osterbrock, D. E., and Raven, P. H., eds., Origins and Extinctions: New Haven, Connecticut, Yale University Press, p. 1-41.}"
}

If the topology and geometry of spacetime are quantum-mechanically variable, then the particular classical large-scale topology and geometry observed in our universe must be statistical predictions of its initial condition. This paper examines the predictions of the ``no boundary'' initial condition for the present large-scale topology and geometry. Finite-action real tunneling solutions of Einstein's equation are important for such predictions. These consist of compact Riemannian (Euclidean) geometries joined to a Lorentzian cosmological geometry across a spacelike surface of vanishing extrinsic curvature. The classification of such solutions is discussed and general constraints on their topology derived. For example, it is shown that, if the Euclidean Ricci tensor is positive, then a real tunneling solution can nucleate only a single connected Lorentzian spacetime (the unique conception theorem). Explicit examples of real tunneling solutions driven by a cosmological constant are exhibited and their implications for cosmic baldness described. It is argued that the most probable large-scale spacetime predicted by the real tunneling solutions of the ``no-boundary'' initial condition has the topology R\ifmmode\times\else\texttimes\fi{}${\mathit{S}}^{3}$ with the de Sitter metric.

@article{doi101103physrevd422458,
    author = "Gibbons, G. W. and Hartle, James B.",
    title = "Real tunneling geometries and the large-scale topology of the universe",
    year = "1990",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
    abstract = "If the topology and geometry of spacetime are quantum-mechanically variable, then the particular classical large-scale topology and geometry observed in our universe must be statistical predictions of its initial condition. This paper examines the predictions of the ``no boundary'' initial condition for the present large-scale topology and geometry. Finite-action real tunneling solutions of Einstein's equation are important for such predictions. These consist of compact Riemannian (Euclidean) geometries joined to a Lorentzian cosmological geometry across a spacelike surface of vanishing extrinsic curvature. The classification of such solutions is discussed and general constraints on their topology derived. For example, it is shown that, if the Euclidean Ricci tensor is positive, then a real tunneling solution can nucleate only a single connected Lorentzian spacetime (the unique conception theorem). Explicit examples of real tunneling solutions driven by a cosmological constant are exhibited and their implications for cosmic baldness described. It is argued that the most probable large-scale spacetime predicted by the real tunneling solutions of the ``no-boundary'' initial condition has the topology R\ifmmode\times\else\texttimes\fi{}${\mathit{S}}^{3}$ with the de Sitter metric.",
    url = "https://doi.org/10.1103/physrevd.42.2458",
    doi = "10.1103/physrevd.42.2458",
    openalex = "W2104986635",
    references = "doi1010079783540743118, doi101007bf02345020, doi1010160370157380901301, doi1010160370269382908668, doi1010160550321388900971, doi101103physrevd152929, doi101103physrevd252065, doi101103physrevd272848, doi101103physrevd282118, doi101103physrevd282960, doi1023071971013"
}

PART I: A THEORY OF ORDER: Science, philosophy, and truth Order and randomness The strong cosmological principle and time's arrow The importance of being discrete Seven steps to quantum physics Alice in quantumland The strong cosmological principle and quantum theory PART II: ASPECTS OF TIMEBOUND ORDER: Cosmic evolution: the standard model Gravitational clustering and structural order Molecules, genes, and evolution Evolution and the growth of order Language, thought, and perception What is consciousness? Mind and body Chance, necessity, and freedom Notes.

@article{doi105860choice275112,
    title = "Cosmogenesis: the growth of order in the universe",
    year = "1990",
    journal = "Choice Reviews Online",
    abstract = "PART I: A THEORY OF ORDER: Science, philosophy, and truth Order and randomness The strong cosmological principle and time's arrow The importance of being discrete Seven steps to quantum physics Alice in quantumland The strong cosmological principle and quantum theory PART II: ASPECTS OF TIMEBOUND ORDER: Cosmic evolution: the standard model Gravitational clustering and structural order Molecules, genes, and evolution Evolution and the growth of order Language, thought, and perception What is consciousness? Mind and body Chance, necessity, and freedom Notes.",
    url = "https://doi.org/10.5860/choice.27-5112",
    doi = "10.5860/choice.27-5112",
    openalex = "W1601774505"
}

@book{maffei1990the4,
    author = "Maffei, P",
    title = "The Universe in Time",
    year = "1990",
    publisher = "Cambridge, Mass., MIT Press, 407 p.; Translated from the Italian edition (Milan, 1982) by M. Giaconni",
    note = "talkorigins\_source = {true}; raw\_reference = {Maffei, P., 1990, The Universe in Time: Cambridge, Mass., MIT Press, 407 p.; Translated from the Italian edition (Milan, 1982) by M. Giaconni.}"
}

A new type of explanatory mechanism is proposed to account for the fact that many of the dimensionless numbers which characterize particle physics and cosmology take unnatural values. It is proposed that all final singularities 'bounce' or tunnel to initial singularities of new universes at which point the dimensionless parameters of the standard models of particle physics and cosmology undergo small random changes. This speculative hypothesis, plus the conventional physics of gravitational collapse, together comprise a mechanism for natural selection, in which those choices of parameters that lead to universes that produce the most black holes during their lifetime are selected for. If our Universe is a typical member of the ensemble that results from many generations of such reproducing universes then it follows that the parameters of our present Universe are near a local maximum of the number of black holes produced per universe. Thus, modifications of the parameters of particle physics and cosmology from their present values should tend to decrease the number of black holes in the universe. Three possible examples of this mechanism are described.

@article{doi1010880264938191016,
    author = "Smolin, Lee",
    title = "Did the Universe evolve?",
    year = "1992",
    journal = "Classical and Quantum Gravity",
    abstract = "A new type of explanatory mechanism is proposed to account for the fact that many of the dimensionless numbers which characterize particle physics and cosmology take unnatural values. It is proposed that all final singularities 'bounce' or tunnel to initial singularities of new universes at which point the dimensionless parameters of the standard models of particle physics and cosmology undergo small random changes. This speculative hypothesis, plus the conventional physics of gravitational collapse, together comprise a mechanism for natural selection, in which those choices of parameters that lead to universes that produce the most black holes during their lifetime are selected for. If our Universe is a typical member of the ensemble that results from many generations of such reproducing universes then it follows that the parameters of our present Universe are near a local maximum of the number of black holes produced per universe. Thus, modifications of the parameters of particle physics and cosmology from their present values should tend to decrease the number of black holes in the universe. Three possible examples of this mechanism are described.",
    url = "https://doi.org/10.1088/0264-9381/9/1/016",
    doi = "10.1088/0264-9381/9/1/016",
    openalex = "W2006208772"
}

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

@article{doi101017s001221730001057x,
    author = "Sullivan, Thomas D.",
    title = "On the Alleged Causeless Beginning of the Universe: A Reply to Quentin Smith",
    year = "1994",
    journal = "Dialogue",
    abstract = "An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.",
    url = "https://doi.org/10.1017/s001221730001057x",
    doi = "10.1017/s001221730001057x",
    openalex = "W2081638908",
    references = "doi101086289415"
}

We consider an alternative scenario of inflation which can account for a spatially open universe. It is similar to the old inflation in which the bubble nucleation occurs in the sea of the false vacuum, but it differs from the old inflation in that the second slow rollover inflation occurs inside a nucleated bubble. Hence, our observable universe is entirely contained in one nucleated bubble. The significance of the scenario is that apart from a variance caused by model parameters, it gives us a definite prediction on the spectrum of the primordial density perturbations, and hence it is observationally testable. Here we investigate the spectrum of cosmic microwave background anisotropies on large angular scales. We find that the contribution from peculiar modes which never appear in the usual harmonic analysis is significant in the case Ω 0 ≲ 0.1.

@article{doi101086176588,
    author = "Yamamoto, Kazuhiro and Sasaki, Misao and Tanaka, Takahiro",
    title = "Large-Angle Cosmic Microwave Background Anisotropy in an Open Universe in the One-Bubble Inflationary Scenario",
    year = "1995",
    journal = "The Astrophysical Journal",
    abstract = "We consider an alternative scenario of inflation which can account for a spatially open universe. It is similar to the old inflation in which the bubble nucleation occurs in the sea of the false vacuum, but it differs from the old inflation in that the second slow rollover inflation occurs inside a nucleated bubble. Hence, our observable universe is entirely contained in one nucleated bubble. The significance of the scenario is that apart from a variance caused by model parameters, it gives us a definite prediction on the spectrum of the primordial density perturbations, and hence it is observationally testable. Here we investigate the spectrum of cosmic microwave background anisotropies on large angular scales. We find that the contribution from peculiar modes which never appear in the usual harmonic analysis is significant in the case Ω 0 ≲ 0.1.",
    url = "https://doi.org/10.1086/176588",
    doi = "10.1086/176588",
    openalex = "W2950545517"
}

Motivated by observational indications of low cosmological mass density, we study a spatially open inflation modified hot big bang model whose evolutionary history is divided into three epochs: an early scalar field inflation epoch and the usual radiation and baryon (nonrelativistic matter) epochs. Generalizing techniques previously developed, we derive general solutions of the relativistic linear peturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from quantum-mechanical initial conditions under the assumption that the perturbations are in the ground state at early times. The constants of integration in the radiation and baryon epoch solutions are determined from joining conditions derived by requiring that the linear perturbation equations remain nonsingular at the transitions between epochs. Expressions are derived for a number of baryon-epoch statistics which characterize large-scale structure, including the fractional mass, peculiar velocity, and gravitational potential perturbation two-point correlation functions, and the mean square value of the fractional mass and peculiar velocity perturbations. The Sachs-Wolfe relation is generalized to the open model and an expression for the angular fluctuation spectrum of the cosmic microwave background radiation temperature anisotropy is derived; we also determine the dipole velocity perturbation two-point correlation function and mean square value.The fractional energy density perturbation power spectrum is not a power law; on small scales we find the usual n=+1 scale-invariant flat model law, while on large scales we discover a n=-1 spectrum. The small-scale part of the fractional mass perturbation two-point correlation function agrees with what one finds in the n=+1 scale-invariant flat case, but it has a second zero and at large scales the fractional mass perturbations are weakly positively correlated. Once again, given the form of the fractional mass perturbations are weakly positively correlated. Once again, given the form of the fractional energy density perturbation power spectrum in this model, we find that the slope of the inflation epoch scalar field potential cannot be unduly constrained by observational data.

@article{doi101103physrevd521837,
    author = "Ratra, Bharat and Peebles, P. J. E.",
    title = "Inflation in an open universe",
    year = "1995",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
    abstract = "Motivated by observational indications of low cosmological mass density, we study a spatially open inflation modified hot big bang model whose evolutionary history is divided into three epochs: an early scalar field inflation epoch and the usual radiation and baryon (nonrelativistic matter) epochs. Generalizing techniques previously developed, we derive general solutions of the relativistic linear peturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from quantum-mechanical initial conditions under the assumption that the perturbations are in the ground state at early times. The constants of integration in the radiation and baryon epoch solutions are determined from joining conditions derived by requiring that the linear perturbation equations remain nonsingular at the transitions between epochs. Expressions are derived for a number of baryon-epoch statistics which characterize large-scale structure, including the fractional mass, peculiar velocity, and gravitational potential perturbation two-point correlation functions, and the mean square value of the fractional mass and peculiar velocity perturbations. The Sachs-Wolfe relation is generalized to the open model and an expression for the angular fluctuation spectrum of the cosmic microwave background radiation temperature anisotropy is derived; we also determine the dipole velocity perturbation two-point correlation function and mean square value.The fractional energy density perturbation power spectrum is not a power law; on small scales we find the usual n=+1 scale-invariant flat model law, while on large scales we discover a n=-1 spectrum. The small-scale part of the fractional mass perturbation two-point correlation function agrees with what one finds in the n=+1 scale-invariant flat case, but it has a second zero and at large scales the fractional mass perturbations are weakly positively correlated. Once again, given the form of the fractional mass perturbations are weakly positively correlated. Once again, given the form of the fractional energy density perturbation power spectrum in this model, we find that the slope of the inflation epoch scalar field potential cannot be unduly constrained by observational data.",
    url = "https://doi.org/10.1103/physrevd.52.1837",
    doi = "10.1103/physrevd.52.1837",
    openalex = "W2019344527"
}

We present a natural scenario for obtaining an open universe (${\mathrm{\ensuremath{\Omega}}}_{0}$1) through inflation. In this scenario, there are two epochs of inflationary expansion---an epoch of ``old inflation,'' during which the inflaton field is stuck in a false vacuum, followed by an epoch of ``new inflation,'' during which the inflation field slowly rolls toward its true minimum. During the first epoch, inflation solves the smoothness and horizon problems. Then an open universe (with negative spatial curvature) is created by the nucleation of a single bubble. In effect \ensuremath{\Omega} is instantaneously ``reset'' to zero. During the subsequent ``new'' inflation \ensuremath{\Omega} rises toward unity. The value of \ensuremath{\Omega} today is calculable in terms of the parameters of the potential, and we show that obtaining values significantly different from zero or unity (though within the range 01) does not require significant fine-tuning. We compute the spectrum of density perturbations by evolving the Bunch-Davies vacuum modes across the bubble wall into its interior.

@article{doi101103physrevd523314,
    author = "Bucher, Martin and Goldhaber, Alfred S. and Turok, Neil",
    title = "Open universe from inflation",
    year = "1995",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
    abstract = "We present a natural scenario for obtaining an open universe (${\mathrm{\ensuremath{\Omega}}}\_{0}$1) through inflation. In this scenario, there are two epochs of inflationary expansion---an epoch of ``old inflation,'' during which the inflaton field is stuck in a false vacuum, followed by an epoch of ``new inflation,'' during which the inflation field slowly rolls toward its true minimum. During the first epoch, inflation solves the smoothness and horizon problems. Then an open universe (with negative spatial curvature) is created by the nucleation of a single bubble. In effect \ensuremath{\Omega} is instantaneously ``reset'' to zero. During the subsequent ``new'' inflation \ensuremath{\Omega} rises toward unity. The value of \ensuremath{\Omega} today is calculable in terms of the parameters of the potential, and we show that obtaining values significantly different from zero or unity (though within the range 01) does not require significant fine-tuning. We compute the spectrum of density perturbations by evolving the Bunch-Davies vacuum modes across the bubble wall into its interior.",
    url = "https://doi.org/10.1103/physrevd.52.3314",
    doi = "10.1103/physrevd.52.3314",
    openalex = "W2159740059"
}

Complexity theory is one of the most controversial areas of current scientific research. Developing out of chaos theory, complexity suggests that there are hidden tendencies in nature to select ordered states, even when statistically they are vastly outnumbered by chaotic possibilities: that there is a deep natural impulse towards order, counteracting the degenerative tendencies of the Second Law of Thermodynamics. Like chaos, complexity is a multidisciplinary area of research and those involved include physicists, economists and biologists. This is a study of complexity.

@article{doi105860choice333294,
    title = "At home in the universe: the search for laws of self-organization and complexity",
    year = "1996",
    journal = "Choice Reviews Online",
    abstract = "Complexity theory is one of the most controversial areas of current scientific research. Developing out of chaos theory, complexity suggests that there are hidden tendencies in nature to select ordered states, even when statistically they are vastly outnumbered by chaotic possibilities: that there is a deep natural impulse towards order, counteracting the degenerative tendencies of the Second Law of Thermodynamics. Like chaos, complexity is a multidisciplinary area of research and those involved include physicists, economists and biologists. This is a study of complexity.",
    url = "https://doi.org/10.5860/choice.33-3294",
    doi = "10.5860/choice.33-3294",
    openalex = "W2100317815",
    references = "doi101007978134901892520, doi1010160020711x94901198, doi10106312809917, doi10106312811091, doi101126science7466396, doi1012019780429496639, doi1023075214, doi105860choice273873, doi105860choice293880, openalexw1528908714"
}

We present spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 z 0.62. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-z Supernova Search Team and recent results by Riess et al., this expanded set of 16 high-redshift M \ 1) methods. We estimate the dynamical age of the universe to be 14.2 ^1.7 Gyr including systematic uncertainties in the current Cepheid distance scale. We estimate the likely e ect of several sources of systematic error, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. Presently, none of these e ects appear to reconcile the data with and) " \ 0 q 0 0.

@article{doi101086300499,
    author = "Riess, Adam G. and Filippenko, A. V. and Challis, P. and Clocchiatti, A. and Diercks, Alan H. and Garnavich, P. and Gilliland, Ron and Hogan, Craig J. and Jha, Saurabh W. and Kirshner, R. and Leibundgut, B. and Phillips, M. M. and Reiss, David J. and Schmidt, B. and Schommer, R. A. and Smith, R. Chris and Spyromilio, J. and Stubbs, C. W. and Suntzeff, N. B. and Tonry, J.",
    title = "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant",
    year = "1998",
    journal = "The Astronomical Journal",
    abstract = {We present spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 z 0.62. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-z Supernova Search Team and recent results by Riess et al., this expanded set of 16 high-redshift M \ 1) methods. We estimate the dynamical age of the universe to be 14.2 ^1.7 Gyr including systematic uncertainties in the current Cepheid distance scale. We estimate the likely e ect of several sources of systematic error, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. Presently, none of these e ects appear to reconcile the data with and) " \ 0 q 0 0.},
    url = "https://doi.org/10.1086/300499",
    doi = "10.1086/300499",
    openalex = "W2073832139"
}

We demonstrate in the context of the minisuperspace model consisting of a closed Friedmann-Robertson-Walker universe coupled to a scalar field that Vilenkin's tunneling wave function can only be consistently defined for particular choices of operator ordering in the Wheeler-DeWitt equation. The requirement of regularity of the wave function has the particular consequence that the probability amplitude, which has been used previously in the literature in discussions of issues such as the prediction of inflation, is likewise ill defined for certain choices of operator ordering with Vilenkin's boundary condition. By contrast, the Hartle-Hawking no-boundary wave function can be consistently defined within these models, independently of operator ordering. The significance of this result is discussed within the context of the debate about the predictions of semiclassical quantum cosmology. In particular, it is argued that inflation cannot be confidently regarded as a ``prediction'' of the tunneling wave function, for reasons similar to those previously invoked in the case of the no-boundary wave function. A synthesis of the no-boundary and tunneling approaches is argued for.

@article{doi101103physrevd59063513,
    author = "Kontoleon, Nectarios and Wiltshire, David L.",
    title = "Operator ordering and consistency of the wave function of the Universe",
    year = "1999",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
    abstract = "We demonstrate in the context of the minisuperspace model consisting of a closed Friedmann-Robertson-Walker universe coupled to a scalar field that Vilenkin's tunneling wave function can only be consistently defined for particular choices of operator ordering in the Wheeler-DeWitt equation. The requirement of regularity of the wave function has the particular consequence that the probability amplitude, which has been used previously in the literature in discussions of issues such as the prediction of inflation, is likewise ill defined for certain choices of operator ordering with Vilenkin's boundary condition. By contrast, the Hartle-Hawking no-boundary wave function can be consistently defined within these models, independently of operator ordering. The significance of this result is discussed within the context of the debate about the predictions of semiclassical quantum cosmology. In particular, it is argued that inflation cannot be confidently regarded as a ``prediction'' of the tunneling wave function, for reasons similar to those previously invoked in the case of the no-boundary wave function. A synthesis of the no-boundary and tunneling approaches is argued for.",
    url = "https://doi.org/10.1103/physrevd.59.063513",
    doi = "10.1103/physrevd.59.063513",
    openalex = "W2146565874",
    references = "doi101103physrevd502581"
}

The cosmic triangle is introduced as a way of representing the past, present, and future status of the universe. Our current location within the cosmic triangle is determined by the answers to three questions: How much matter is in the universe? Is the expansion rate slowing down or speeding up? And, is the universe flat? A review of recent observations suggests a universe that is lightweight (matter density about one-third the critical value), is accelerating, and is flat. The acceleration implies the existence of cosmic dark energy that overcomes the gravitational self-attraction of matter and causes the expansion to speed up.

@article{doi101126science28454191481,
    author = "Bahcall, Neta A. and Ostriker, Jeremiah P. and Perlmutter, S. and Steinhardt, Paul J.",
    title = "The Cosmic Triangle: Revealing the State of the Universe",
    year = "1999",
    journal = "Science",
    abstract = "The cosmic triangle is introduced as a way of representing the past, present, and future status of the universe. Our current location within the cosmic triangle is determined by the answers to three questions: How much matter is in the universe? Is the expansion rate slowing down or speeding up? And, is the universe flat? A review of recent observations suggests a universe that is lightweight (matter density about one-third the critical value), is accelerating, and is flat. The acceleration implies the existence of cosmic dark energy that overcomes the gravitational self-attraction of matter and causes the expansion to speed up.",
    url = "https://doi.org/10.1126/science.284.5419.1481",
    doi = "10.1126/science.284.5419.1481",
    openalex = "W2060566384",
    references = "doi101073pnas153168"
}

All physical systems register and process information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The Universe is a physical system. The amount of information that the Universe can register and the number of elementary operations that it can have performed over its history are calculated. The Universe can have performed 10(120) ops on 10(90) bits (10(120) bits including gravitational degrees of freedom).

@article{doi101103physrevlett88237901,
    author = "Lloyd, Seth",
    title = "Computational Capacity of the Universe",
    year = "2002",
    journal = "Physical Review Letters",
    abstract = "All physical systems register and process information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The Universe is a physical system. The amount of information that the Universe can register and the number of elementary operations that it can have performed over its history are calculated. The Universe can have performed 10(120) ops on 10(90) bits (10(120) bits including gravitational degrees of freedom).",
    url = "https://doi.org/10.1103/physrevlett.88.237901",
    doi = "10.1103/physrevlett.88.237901",
    openalex = "W1993466133",
    references = "doi10103835023282"
}

@article{doi101016jphysletb200412067,
    author = "Ambjørn, J. and Jurkiewicz, J. and Loll, R.",
    title = "Semiclassical universe from first principles",
    year = "2004",
    journal = "Physics Letters B",
    url = "https://doi.org/10.1016/j.physletb.2004.12.067",
    doi = "10.1016/j.physletb.2004.12.067",
    openalex = "W1970459282",
    references = "doi101103physrevd502581"
}

We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time.

@article{doi101103physrevd72064014,
    author = "Ambjørn, J. and Jurkiewicz, J. and Loll, R.",
    title = "Reconstructing the Universe",
    year = "2005",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology",
    abstract = "We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time.",
    url = "https://doi.org/10.1103/physrevd.72.064014",
    doi = "10.1103/physrevd.72.064014",
    openalex = "W2167377764",
    references = "doi101103physrevd502581"
}

In three spacetime dimensions, general relativity drastically simplifies, becoming a "topological" theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2 + 1)-dimensional vacuum gravity in the setting of a spatially closed universe.

@article{doi1012942lrr20051,
    author = "Carlip, Steven",
    title = "Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe",
    year = "2005",
    journal = "Living Reviews in Relativity",
    abstract = {In three spacetime dimensions, general relativity drastically simplifies, becoming a "topological" theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2 + 1)-dimensional vacuum gravity in the setting of a spatially closed universe.},
    url = "https://doi.org/10.12942/lrr-2005-1",
    doi = "10.12942/lrr-2005-1",
    openalex = "W2109193263",
    references = "doi101103physrevd422458"
}

@incollection{doi10100797835407347892,
    title = "The Large-Scale Structure of the Universe",
    year = "2007",
    booktitle = "Astronomy and astrophysics library",
    url = "https://doi.org/10.1007/978-3-540-73478-9\_2",
    doi = "10.1007/978-3-540-73478-9\_2",
    openalex = "W2981570800"
}

@article{doi101007s1070100791869,
    author = "Tegmark, Max",
    title = "The Mathematical Universe",
    year = "2007",
    journal = "Foundations of Physics",
    url = "https://doi.org/10.1007/s10701-007-9186-9",
    doi = "10.1007/s10701-007-9186-9",
    openalex = "W1966058685",
    references = "doi1010079783540680017, doi101016s0308596199000646, doi10108800319112382028, doi101103physrevlett97191302, doi1011111467921300309, doi10230720049291, openalexw1489050524"
}

Ten years ago, the discovery that the expansion of the universe is accelerating put in place the last major building block of the present cosmological model, in which the universe is composed of 4% baryons, 20% dark matter, and 76% dark energy. At the same time, it posed one of the most profound mysteries in all of science, with deep connections to both astrophysics and particle physics. Cosmic acceleration could arise from the repulsive gravity of dark energy—for example, the quantum energy of the vacuum—or it may signal that general relativity (GR) breaks down on cosmological scales and must be replaced. We review the present observational evidence for cosmic acceleration and what it has revealed about dark energy, discuss the various theoretical ideas that have been proposed to explain acceleration, and describe the key observational probes that will shed light on this enigma in the coming years.

@article{doi101146annurevastro46060407145243,
    author = "Frieman, J. and Turner, Michael S. and Huterer, Dragan",
    title = "Dark Energy and the Accelerating Universe",
    year = "2008",
    journal = "Annual Review of Astronomy and Astrophysics",
    abstract = "Ten years ago, the discovery that the expansion of the universe is accelerating put in place the last major building block of the present cosmological model, in which the universe is composed of 4\% baryons, 20\% dark matter, and 76\% dark energy. At the same time, it posed one of the most profound mysteries in all of science, with deep connections to both astrophysics and particle physics. Cosmic acceleration could arise from the repulsive gravity of dark energy—for example, the quantum energy of the vacuum—or it may signal that general relativity (GR) breaks down on cosmological scales and must be replaced. We review the present observational evidence for cosmic acceleration and what it has revealed about dark energy, discuss the various theoretical ideas that have been proposed to explain acceleration, and describe the key observational probes that will shed light on this enigma in the coming years.",
    url = "https://doi.org/10.1146/annurev.astro.46.060407.145243",
    doi = "10.1146/annurev.astro.46.060407.145243",
    openalex = "W2102197207",
    references = "doi101073pnas153168, doi10108811266708200006006, doi101093mnras1085372, doi101103physrevd68023509, doi101103physrevlett592607, doi105860choice311499, openalexw3098371892"
}

This philosophical paper explores the relation between modern scientific simulations and the future of the universe. We argue that a simulation of an entire universe will result from future scientific activity. This requires us to tackle the challenge of simulating open-ended evolution at all levels in a single simulation. The simulation should encompass not only biological evolution, but also physical evolution (a level below) and cultural evolution (a level above). The simulation would allow us to probe what would happen if we would "replay the tape of the universe" with the same or different laws and initial conditions. We also distinguish between real-world and artificial-world modelling. Assuming that intelligent life could indeed simulate an entire universe, this leads to two tentative hypotheses. Some authors have argued that we may already be in a simulation run by an intelligent entity. Or, if such a simulation could be made real, this would lead to the production of a new universe. This last direction is argued with a careful speculative philosophical approach, emphasizing the imperative to find a solution to the heat death problem in cosmology. The reader is invited to consult Annex 1 for an overview of the logical structure of this paper. -- Keywords: far future, future of science, ALife, simulation, realization, cosmology, heat death, fine-tuning, physical eschatology, cosmological natural selection, cosmological artificial selection, artificial cosmogenesis, selfish biocosm hypothesis, meduso-anthropic principle, developmental singularity hypothesis, role of intelligent life.

@misc{doi1048550arxiv08031087,
    author = "Vidal, Clément",
    title = "The Future of Scientific Simulations: from Artificial Life to Artificial Cosmogenesis",
    year = "2008",
    booktitle = "ArXiv.org",
    abstract = {This philosophical paper explores the relation between modern scientific simulations and the future of the universe. We argue that a simulation of an entire universe will result from future scientific activity. This requires us to tackle the challenge of simulating open-ended evolution at all levels in a single simulation. The simulation should encompass not only biological evolution, but also physical evolution (a level below) and cultural evolution (a level above). The simulation would allow us to probe what would happen if we would "replay the tape of the universe" with the same or different laws and initial conditions. We also distinguish between real-world and artificial-world modelling. Assuming that intelligent life could indeed simulate an entire universe, this leads to two tentative hypotheses. Some authors have argued that we may already be in a simulation run by an intelligent entity. Or, if such a simulation could be made real, this would lead to the production of a new universe. This last direction is argued with a careful speculative philosophical approach, emphasizing the imperative to find a solution to the heat death problem in cosmology. The reader is invited to consult Annex 1 for an overview of the logical structure of this paper. -- Keywords: far future, future of science, ALife, simulation, realization, cosmology, heat death, fine-tuning, physical eschatology, cosmological natural selection, cosmological artificial selection, artificial cosmogenesis, selfish biocosm hypothesis, meduso-anthropic principle, developmental singularity hypothesis, role of intelligent life.},
    url = "https://doi.org/10.48550/arxiv.0803.1087",
    doi = "10.48550/arxiv.0803.1087",
    openalex = "W1582948755",
    references = "doi101007bf02084158, doi10103835023282, doi101038nature03597, doi10106312820190, doi1010631881299, doi1011111467921300309, doi10230720031996, doi105860choice273873, openalexw1489050524, openalexw1522029621"
}

@article{doi101007s1069901091849,
    author = "Stewart, John E.",
    title = "The Meaning of Life in a Developing Universe",
    year = "2010",
    journal = "Foundations of Science",
    url = "https://doi.org/10.1007/s10699-010-9184-9",
    doi = "10.1007/s10699-010-9184-9",
    openalex = "W1982582256",
    references = "doi1010160019103575901712, doi1010160022519364900384, doi101086406755, doi101093oso97801985029440010001, doi101111j155856461995tb04464x, doi1015159781400820108, doi1015159781400858712, doi1023071351721, doi1048550arxiv08031087, openalexw2040525210, openalexw2624262714"
}

This paper presents a simple and purely geometrical Grand Unification Theory. Quantum Gravity, Electrostatic and Magnetic interactions are shown in a unified framework. Newton’s, Gauss’ and Biot‐Savart’s Laws are derived from first principles. Unification symmetry is defined for all the existing forces. This alternative model does not require Strong and Electroweak forces. A 4D Shock ‐Wave Hyperspherical topology is proposed for the Universe which together with a Quantum Lagrangian Principle and a Dilator based model for matter result in a quantized stepwise expansion for the whole Universe along a radial direction within a 4D spatial manifold. The Hypergeometrical Standard Model for matter, Universe Topology and a new Law of Gravitation are presented.

@article{doi10106313536448,
    author = "Pereira, Marco A.",
    title = "The Hypergeometrical Universe: Cosmology and Standard Model",
    year = "2010",
    journal = "AIP conference proceedings",
    abstract = "This paper presents a simple and purely geometrical Grand Unification Theory. Quantum Gravity, Electrostatic and Magnetic interactions are shown in a unified framework. Newton’s, Gauss’ and Biot‐Savart’s Laws are derived from first principles. Unification symmetry is defined for all the existing forces. This alternative model does not require Strong and Electroweak forces. A 4D Shock ‐Wave Hyperspherical topology is proposed for the Universe which together with a Quantum Lagrangian Principle and a Dilator based model for matter result in a quantized stepwise expansion for the whole Universe along a radial direction within a 4D spatial manifold. The Hypergeometrical Standard Model for matter, Universe Topology and a new Law of Gravitation are presented.",
    url = "https://doi.org/10.1063/1.3536448",
    doi = "10.1063/1.3536448",
    openalex = "W2037727759",
    references = "doi10106311580037, openalexw9793639"
}

We propose a model of inflation with a suitable potential for a single scalar field which falls in the wide class of hilltop inflation. We derive the analytical expressions for most of the physical quantities related to inflation and show that all of them represent the true behavior as required from a model of inflation. We further subject the results to observational verification by formulating the theory of perturbations based on our model followed by an estimation for the values of those observable parameters. Our model is found to be in excellent agreement with observational data. Thus, the features related to the model leads us to infer that this type of hilltop inflation may be a natural choice for explaining the early universe.

@article{doi10108814757516201001029,
    author = "Pal, Barun Kumar and Pal, Supratik and Basu, Banasri",
    title = "Mutated hilltop inflation: a natural choice for early universe",
    year = "2010",
    journal = "Journal of Cosmology and Astroparticle Physics",
    abstract = "We propose a model of inflation with a suitable potential for a single scalar field which falls in the wide class of hilltop inflation. We derive the analytical expressions for most of the physical quantities related to inflation and show that all of them represent the true behavior as required from a model of inflation. We further subject the results to observational verification by formulating the theory of perturbations based on our model followed by an estimation for the values of those observable parameters. Our model is found to be in excellent agreement with observational data. Thus, the features related to the model leads us to infer that this type of hilltop inflation may be a natural choice for explaining the early universe.",
    url = "https://doi.org/10.1088/1475-7516/2010/01/029",
    doi = "10.1088/1475-7516/2010/01/029",
    openalex = "W2006734755",
    references = "doi101103physrevlett77215"
}

@article{doi101016jactaastro201111006,
    author = "Smart, John M.",
    title = "The transcension hypothesis: Sufficiently advanced civilizations invariably leave our universe, and implications for METI and SETI",
    year = "2011",
    journal = "Acta Astronautica",
    url = "https://doi.org/10.1016/j.actaastro.2011.11.006",
    doi = "10.1016/j.actaastro.2011.11.006",
    openalex = "W2050361934",
    references = "doi101017cbo9780511790881, doi101017cbo9781139164245, doi101073pnas0507655102, doi10114510818701081893, doi1023071425268, doi10230720031996, doi1048550arxiv08031087, doi105860choice275886, doi105860choice396411, doi105860choice495144, openalexw1618666643, openalexw2340966270"
}

@incollection{doi101007978364235482313,
    author = "Vidal, Clément",
    title = "Artificial Cosmogenesis: A New Kind of Cosmology",
    year = "2012",
    booktitle = "Emergence, complexity and computation",
    url = "https://doi.org/10.1007/978-3-642-35482-3\_13",
    doi = "10.1007/978-3-642-35482-3\_13",
    openalex = "W1942536279",
    references = "doi101007s1069901092183"
}

We review observational evidence for a matter-antimatter asymmetry in the early universe, which leads to the remnant matter density we observe today. We also discuss bounds on the presence of antimatter in the present-day universe, including the possibility of a large lepton asymmetry in the cosmic neutrino background. We briefly review the theoretical framework within which baryogenesis, the dynamical generation of a matter-antimatter asymmetry, can occur. As an example, we discuss a testable minimal particle physics model that simultaneously explains the baryon asymmetry of the universe, neutrino oscillations and dark matter.

@article{doi10108813672630149095012,
    author = "Canetti, Laurent and Drewes, Marco and Shaposhnikov, Mikhail",
    title = "Matter and antimatter in the universe",
    year = "2012",
    journal = "New Journal of Physics",
    abstract = "We review observational evidence for a matter-antimatter asymmetry in the early universe, which leads to the remnant matter density we observe today. We also discuss bounds on the presence of antimatter in the present-day universe, including the possibility of a large lepton asymmetry in the cosmic neutrino background. We briefly review the theoretical framework within which baryogenesis, the dynamical generation of a matter-antimatter asymmetry, can occur. As an example, we discuss a testable minimal particle physics model that simultaneously explains the baryon asymmetry of the universe, neutrino oscillations and dark matter.",
    url = "https://doi.org/10.1088/1367-2630/14/9/095012",
    doi = "10.1088/1367-2630/14/9/095012",
    openalex = "W1977127359",
    references = "doi101007bf01332580"
}

In an open Friedmann-Robertson-Walker (FRW) space background, we study the classical and quantum cosmological models in the framework of the recently proposed nonlinear massive gravity theory. Although the constraints which are present in this theory prevent it from admitting the flat and closed FRW models as its cosmological solutions, for the open FRW universe it is not the case. We have shown that, either in the absence of matter or in the presence of a perfect fluid, the classical field equations of such a theory adopt physical solutions for the open FRW model, in which the mass term shows itself as a cosmological constant. These classical solutions consist of two distinguishable branches: One is a contacting universe which tends to a future singularity with zero size, while another is an expanding universe having a past singularity from which it begins its evolution. A classically forbidden region separates these two branches from each other. We then employ the familiar canonical quantization procedure in the given cosmological setting to find the cosmological wave functions. We use the resulting wave function to investigate the possibility of the avoidance of classical singularities due to quantum effects. It is shown that the quantum expectation values of the scale factor, although they have either contracting or expanding phases like their classical counterparts, are not disconnected from each other. Indeed, the classically forbidden region may be replaced by a bouncing period in which the scale factor bounces from the contraction to its expansion eras. Using the Bohmian approach of quantum mechanics, we also compute the Bohmian trajectory and the quantum potential related to the system, which their analysis shows are the direct effects of the mass term on the dynamics of the universe.

@article{doi101103physrevd85083529,
    author = "Vakili, Babak and Khosravi, Nima",
    title = "Classical and quantum massive cosmology for the open FRW universe",
    year = "2012",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology",
    abstract = "In an open Friedmann-Robertson-Walker (FRW) space background, we study the classical and quantum cosmological models in the framework of the recently proposed nonlinear massive gravity theory. Although the constraints which are present in this theory prevent it from admitting the flat and closed FRW models as its cosmological solutions, for the open FRW universe it is not the case. We have shown that, either in the absence of matter or in the presence of a perfect fluid, the classical field equations of such a theory adopt physical solutions for the open FRW model, in which the mass term shows itself as a cosmological constant. These classical solutions consist of two distinguishable branches: One is a contacting universe which tends to a future singularity with zero size, while another is an expanding universe having a past singularity from which it begins its evolution. A classically forbidden region separates these two branches from each other. We then employ the familiar canonical quantization procedure in the given cosmological setting to find the cosmological wave functions. We use the resulting wave function to investigate the possibility of the avoidance of classical singularities due to quantum effects. It is shown that the quantum expectation values of the scale factor, although they have either contracting or expanding phases like their classical counterparts, are not disconnected from each other. Indeed, the classically forbidden region may be replaced by a bouncing period in which the scale factor bounces from the contraction to its expansion eras. Using the Bohmian approach of quantum mechanics, we also compute the Bohmian trajectory and the quantum potential related to the system, which their analysis shows are the direct effects of the mass term on the dynamics of the universe.",
    url = "https://doi.org/10.1103/physrevd.85.083529",
    doi = "10.1103/physrevd.85.083529",
    openalex = "W2021852171",
    references = "doi101103physrevd61063501"
}

The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky view of the surface of last scattering available to date. This allows us to detect possible departures from the standard model of a globally homogeneous and isotropic cosmology on the largest scales. We search for correlations induced by a possible non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance χrec), both via a direct search for matched circular patterns at the intersections and by an optimal likelihood search for specific topologies. For the latter we consider flat spaces with cubic toroidal (T3), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature spaces. These searches yield no detection of the compact topology with the scale below the diameter of the last scattering surface. For most compact topologies studied the likelihood maximized over the orientation of the space relative to the observed map shows some preference for multi-connected models just larger than the diameter of the last scattering surface. Since this effect is also present in simulated realizations of isotropic maps, we interpret it as the inevitable alignment of mild anisotropic correlations with chance features in a single sky realization; such a feature can also be present, in milder form, when the likelihood is marginalized over orientations. Thus marginalized, the limits on the radius ℛi of the largest sphere inscribed in topological domain (at log-likelihood-ratio Δln ℒ > −5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, ℛi> 0.92χrec for the T3 cubic torus; ℛi> 0.71χrec for the T2 chimney; ℛi> 0.50χrec for the T1 slab; and in a positively curved Universe, ℛi> 1.03χrec for the dodecahedral space; ℛi> 1.0χrec for the truncated cube; and ℛi> 0.89χrec for the octahedral space. The limit for a wider class of topologies, i.e., those predicting matching pairs of back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles search, is ℛi> 0.94χrec at 99% confidence level. Similar limits apply to a wide, although not exhaustive, range of topologies. We also perform a Bayesian search for an anisotropic global Bianchi VIIh geometry. In the non-physical setting where the Bianchi cosmology is decoupled from the standard cosmology, Planck data favour the inclusion of a Bianchi component with a Bayes factor of at least 1.5 units of log-evidence. Indeed, the Bianchi pattern is quite efficient at accounting for some of the large-scale anomalies found in Planck data. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. In the physically motivated setting where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VIIh cosmology and constrain the vorticity of such models to (ω/H)0< 8.1 × 10-10 (95% confidence level).

@article{doi10105100046361201321546,
    author = "Ade, P. A. R. and Aghanim, N. and Armitage-Caplan, C. and Arnaud, M. and Ashdown, M. and Atrio‐Barandela, F. and Aumont, J. and Baccigalupi, C. and Banday, A. J. and Barreiro, R. B. and Bartlett, J. G. and Battaner, E. and Benabed, K. and Benoît, A. and Benoit-Lévy, A. and Bernard, J.-P. and Bersanelli, M. and Bielewicz, P. and Bobin, J. and Bock, J. J. and Bonaldi, A. and Bonavera, L. and Bond, J. R. and Borrill, J. and Bouchet, F. R. and Bridges, M. and Bucher, M. and Burigana, C. and Butler, R. C. and Cardoso, J.-F. and Catalano, A. and Challinor, A. and Chamballu, A. and Chiang, H. C. and Chiang, L.-Y and Christensen, P. R. and Church, S. and Clements, D. L. and Colombi, S. and Colombo, L. P. L. and Couchot, F. and Coulais, A. and Crill, B. P. and Curto, A. and Cuttaia, F. and Danese, L. and Davies, R. D. and Davis, R. J. and de Bernardis, P. and de Rosa, A. and de Zotti, G. and Delabrouille, J. and Delouis, J.‐M. and Désert, F.–X. and Diego, J. M. and Dole, H. and Donzelli, S. and Doré, O. and Douspis, M. and Dupac, X. and Efstathiou, G. and Enßlin, T. A. and Eriksen, H. K. and Fabre, O. and Finelli⋆, F. and Forni, O. and Frailis, M. and Franceschi, E. and Galeotta, S. and Ganga, K. and Giard, M. and Giardino, G. and Giraud–Héraud, Y. and González-Nuevo, J. and Górski, K. M. and Golec, Joseph E. and Gregorio, A. and Gruppuso, A. and Hansen, F. K. and Hanson, D. and Harrison, D. L. and Henrot–Versillé, S. and Hernández–Monteagudo, C. and Herranz, D. and Hildebrandt, S. R. and Hivon, E. and Hobson, M. and Holmes, W. A. and Hornstrup, A. and Hovest, W. and Huffenberger, K. M. and Jaffe, A. H. and Jaffe, T. R. and Jones, W. C. and Juvela, M. and Keihänen, E. and Keskitalo, R. and Kisner, T. S. and Knoche, J. and Knox, L.",
    title = "Planck 2013 results. XXVI. Background geometry and topology of the Universe",
    year = "2014",
    journal = "Astronomy and Astrophysics",
    abstract = "The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky view of the surface of last scattering available to date. This allows us to detect possible departures from the standard model of a globally homogeneous and isotropic cosmology on the largest scales. We search for correlations induced by a possible non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance χrec), both via a direct search for matched circular patterns at the intersections and by an optimal likelihood search for specific topologies. For the latter we consider flat spaces with cubic toroidal (T3), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature spaces. These searches yield no detection of the compact topology with the scale below the diameter of the last scattering surface. For most compact topologies studied the likelihood maximized over the orientation of the space relative to the observed map shows some preference for multi-connected models just larger than the diameter of the last scattering surface. Since this effect is also present in simulated realizations of isotropic maps, we interpret it as the inevitable alignment of mild anisotropic correlations with chance features in a single sky realization; such a feature can also be present, in milder form, when the likelihood is marginalized over orientations. Thus marginalized, the limits on the radius ℛi of the largest sphere inscribed in topological domain (at log-likelihood-ratio Δln ℒ > −5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, ℛi> 0.92χrec for the T3 cubic torus; ℛi> 0.71χrec for the T2 chimney; ℛi> 0.50χrec for the T1 slab; and in a positively curved Universe, ℛi> 1.03χrec for the dodecahedral space; ℛi> 1.0χrec for the truncated cube; and ℛi> 0.89χrec for the octahedral space. The limit for a wider class of topologies, i.e., those predicting matching pairs of back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles search, is ℛi> 0.94χrec at 99\% confidence level. Similar limits apply to a wide, although not exhaustive, range of topologies. We also perform a Bayesian search for an anisotropic global Bianchi VIIh geometry. In the non-physical setting where the Bianchi cosmology is decoupled from the standard cosmology, Planck data favour the inclusion of a Bianchi component with a Bayes factor of at least 1.5 units of log-evidence. Indeed, the Bianchi pattern is quite efficient at accounting for some of the large-scale anomalies found in Planck data. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. In the physically motivated setting where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VIIh cosmology and constrain the vorticity of such models to (ω/H)0< 8.1 × 10-10 (95\% confidence level).",
    url = "https://doi.org/10.1051/0004-6361/201321546",
    doi = "10.1051/0004-6361/201321546",
    openalex = "W2163930527",
    references = "doi101016037015739400085h, doi10108802649381159013, doi101103physrevd61063501"
}

We introduce the Illustris Project, a series of large-scale hydrodynamical simulations of galaxy formation. The highest resolution simulation, Illustris-1, covers a volume of (106.5 Mpc) 3, has a dark mass resolution of 6.26 × 10 6 M⊙, and an initial baryonic matter mass resolution of 1.26 × 10 6 M⊙. At z = 0 gravitational forces are softened on scales of 710 pc, and the smallest hydrodynamical gas cells have an extent of 48 pc. We follow the dynamical evolution of 2 × 1820 3 resolution elements and in addition passively evolve 1820 3 Monte Carlo tracer particles reaching a total particle count of more than 18 billion. The galaxy formation model includes: Primordial and metal-line cooling with self-shielding corrections, stellar evolution, stellar feedback, gas recycling, chemical enrichment, supermassive black hole growth, and feedback from active galactic nuclei. Here we describe the simulation suite, and contrast basic predictions of our model for the present-day galaxy population with observations of the local universe. At z = 0 our simulation volume contains about 40 000 well-resolved galaxies covering a diverse range of morphologies and colours including early-type, late-type and irregular galaxies. The simulation reproduces reasonably well the cosmic star formation rate density, the galaxy luminosity function, and baryon conversion efficiency at z = 0. It also qualitatively captures the impact of galaxy environment on the red fractions of galaxies. The internal velocity structure of selected well-resolved disc galaxies obeys the stellar and baryonic Tully-Fisher relation together with flat circular velocity curves. In the well-resolved regime, the simulation reproduces the observed mix of early-type and late-type galaxies. Our model predicts a halo mass dependent impact of baryonic effects on the halo mass function and the masses of haloes caused by feedback from supernova and active galactic nuclei.

@article{doi101093mnrasstu1536,
    author = "Vogelsberger, Mark and Genel, Shy and Springel, Volker and Torrey, Paul and Sijacki, Debora and Xu, D. and Snyder, Greg and Nelson, Dylan and Hernquist, Lars",
    title = "Introducing the Illustris Project: simulating the coevolution of dark and visible matter in the Universe",
    year = "2014",
    journal = "Monthly Notices of the Royal Astronomical Society",
    abstract = "We introduce the Illustris Project, a series of large-scale hydrodynamical simulations of galaxy formation. The highest resolution simulation, Illustris-1, covers a volume of (106.5 Mpc) 3, has a dark mass resolution of 6.26 × 10 6 M⊙, and an initial baryonic matter mass resolution of 1.26 × 10 6 M⊙. At z = 0 gravitational forces are softened on scales of 710 pc, and the smallest hydrodynamical gas cells have an extent of 48 pc. We follow the dynamical evolution of 2 × 1820 3 resolution elements and in addition passively evolve 1820 3 Monte Carlo tracer particles reaching a total particle count of more than 18 billion. The galaxy formation model includes: Primordial and metal-line cooling with self-shielding corrections, stellar evolution, stellar feedback, gas recycling, chemical enrichment, supermassive black hole growth, and feedback from active galactic nuclei. Here we describe the simulation suite, and contrast basic predictions of our model for the present-day galaxy population with observations of the local universe. At z = 0 our simulation volume contains about 40 000 well-resolved galaxies covering a diverse range of morphologies and colours including early-type, late-type and irregular galaxies. The simulation reproduces reasonably well the cosmic star formation rate density, the galaxy luminosity function, and baryon conversion efficiency at z = 0. It also qualitatively captures the impact of galaxy environment on the red fractions of galaxies. The internal velocity structure of selected well-resolved disc galaxies obeys the stellar and baryonic Tully-Fisher relation together with flat circular velocity curves. In the well-resolved regime, the simulation reproduces the observed mix of early-type and late-type galaxies. Our model predicts a halo mass dependent impact of baryonic effects on the halo mass function and the masses of haloes caused by feedback from supernova and active galactic nuclei.",
    url = "https://doi.org/10.1093/mnras/stu1536",
    doi = "10.1093/mnras/stu1536",
    openalex = "W2204815181",
    references = "doi101038nature03597, doi1010880004637x7211193"
}

Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially expanding, highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the inhomogeneities is comparable to the initial Hubble length, and overdense regions collapse and form black holes, because underdense regions continue expanding, allowing inflation to eventually begin. This establishes that inflation can arise from highly inhomogeneous initial conditions and solve the horizon and flatness problems, at least as long as the variations in the scalar field do not include values that exceed the inflationary plateau.

@article{doi10108814757516201609010,
    author = "East, William E. and Kleban, Matthew and Linde, Andrei and Senatore, Leonardo",
    title = "Beginning inflation in an inhomogeneous universe",
    year = "2016",
    journal = "Journal of Cosmology and Astroparticle Physics",
    abstract = "Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially expanding, highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the inhomogeneities is comparable to the initial Hubble length, and overdense regions collapse and form black holes, because underdense regions continue expanding, allowing inflation to eventually begin. This establishes that inflation can arise from highly inhomogeneous initial conditions and solve the horizon and flatness problems, at least as long as the variations in the scalar field do not include values that exceed the inflationary plateau.",
    url = "https://doi.org/10.1088/1475-7516/2016/09/010",
    doi = "10.1088/1475-7516/2016/09/010",
    openalex = "W2218756649",
    references = "doi101103physrevd61063501, doi101103physrevlett77215"
}

This paper presents a simple and purely geometrical Grand Unification Theory.\nQuantum Gravity, Electrostatic and Magnetic interactions are shown in a unified\nframework. Newton’s Gravitational Law, Gauss’ Electrostatics Law and\nBiot-Savart’s Electromagnetism Law are derived from first principles.\nGravitational Lensing, Mercury Perihelion Precession are replicated within the\ntheory. Unification symmetry is defined for all the existing forces. This\nalternative model does not require Strong and Electroweak forces. A 4D\nShock-Wave Hyperspherical topology is proposed for the Universe which together\nwith a Quantum Lagrangian Principle and a Dilator based model for matter result\nin a quantized stepwise expansion for the whole Universe along a radial\ndirection within a 4D spatial manifold. The Hypergeometrical Standard Model for\nmatter, Universe Topology, Simple Cosmogenesis and a new Law of Gravitation are\npresented. Type 1A Supernova Survey HU results is provided. A New de-Broglie\nForce is proposed.

@article{doi104172173643371000248,
    author = "MA, Pereira",
    title = "The Hypergeometrical Universe: Cosmogenesis, Cosmology and Standard Model",
    year = "2016",
    journal = "Journal of Generalized Lie Theory and Applications",
    abstract = "This paper presents a simple and purely geometrical Grand Unification Theory.\nQuantum Gravity, Electrostatic and Magnetic interactions are shown in a unified\nframework. Newton’s Gravitational Law, Gauss’ Electrostatics Law and\nBiot-Savart’s Electromagnetism Law are derived from first principles.\nGravitational Lensing, Mercury Perihelion Precession are replicated within the\ntheory. Unification symmetry is defined for all the existing forces. This\nalternative model does not require Strong and Electroweak forces. A 4D\nShock-Wave Hyperspherical topology is proposed for the Universe which together\nwith a Quantum Lagrangian Principle and a Dilator based model for matter result\nin a quantized stepwise expansion for the whole Universe along a radial\ndirection within a 4D spatial manifold. The Hypergeometrical Standard Model for\nmatter, Universe Topology, Simple Cosmogenesis and a new Law of Gravitation are\npresented. Type 1A Supernova Survey HU results is provided. A New de-Broglie\nForce is proposed.",
    url = "https://doi.org/10.4172/1736-4337.1000248",
    doi = "10.4172/1736-4337.1000248",
    openalex = "W2568121053",
    references = "doi101007bf01332580, doi101016c20090146081, doi10106311580037, doi10106313050989, doi101073pnas153168, doi10111911934936, doi102307jctv131bv375, doi104172173643371000248, openalexw9793639"
}

This paper presents a simple and purely geometrical Grand Unification Theory. Quantum Gravity, Electrostatic and Magnetic interactions are shown in a unified framework. Newton's Gravitational Law, Gauss' Electrostatics Law and Biot-Savart's Electromagnetism Law are derived from first principles. Gravitational Lensing and Mercury Perihelion Precession are replicated within the theory. Unification symmetry is defined for all the existing forces. This alternative model does not require Strong and Electroweak forces. A 4D Shock-Wave Hyperspherical topology is proposed for the Universe which together with a Quantum Lagrangian Principle and a Dilator based model for matter result in a quantized stepwise expansion for the whole Universe along a radial direction within a 4D spatial manifold. The Hypergeometrical Standard Model for matter, Universe Topology and a new Law of Gravitation are presented. Newton's and Einstein's Laws of Gravitation and Dynamics, Gauss Law of Electrostatics among others are challenged when HU presents Type 1A Supernova Survey results. HU's SN1a results challenge current Cosmological Standard Model (L-CDM) by challenging its Cosmological Ruler d(z). SDSS BOSS dataset is shown to support a new Cosmogenesis theory and HU proposal that we are embedded in a 5D Spacetime. The Big Bang Theory is shown to be challenged by SDSS BOSS dataset. Hyperspherical Acoustic Oscillations are demonstrated in the SDSS BOSS Galaxy density. A New de-Broglie Force is proposed.

@misc{openalexw2953388962,
    author = "Pereira, Marco",
    title = "The Hypergeometrical Universe: Cosmogenesis, Cosmology and Standard Model",
    year = "2017",
    booktitle = "viXra",
    abstract = "This paper presents a simple and purely geometrical Grand Unification Theory. Quantum Gravity, Electrostatic and Magnetic interactions are shown in a unified framework. Newton's Gravitational Law, Gauss' Electrostatics Law and Biot-Savart's Electromagnetism Law are derived from first principles. Gravitational Lensing and Mercury Perihelion Precession are replicated within the theory. Unification symmetry is defined for all the existing forces. This alternative model does not require Strong and Electroweak forces. A 4D Shock-Wave Hyperspherical topology is proposed for the Universe which together with a Quantum Lagrangian Principle and a Dilator based model for matter result in a quantized stepwise expansion for the whole Universe along a radial direction within a 4D spatial manifold. The Hypergeometrical Standard Model for matter, Universe Topology and a new Law of Gravitation are presented. Newton's and Einstein's Laws of Gravitation and Dynamics, Gauss Law of Electrostatics among others are challenged when HU presents Type 1A Supernova Survey results. HU's SN1a results challenge current Cosmological Standard Model (L-CDM) by challenging its Cosmological Ruler d(z). SDSS BOSS dataset is shown to support a new Cosmogenesis theory and HU proposal that we are embedded in a 5D Spacetime. The Big Bang Theory is shown to be challenged by SDSS BOSS dataset. Hyperspherical Acoustic Oscillations are demonstrated in the SDSS BOSS Galaxy density. A New de-Broglie Force is proposed.",
    url = "https://openalex.org/W2953388962",
    openalex = "W2953388962"
}

The tunneling wave function of the universe is investigated in a minisuperspace framework of a de Sitter universe with a quantum scalar field, treated as a perturbation. We consider three different approaches to defining the tunneling wave function: (1) tunneling boundary conditions in superspace, (2) Lorentzian path integral, and (3) quantum tunneling from initial universe of a vanishing size. We show that the superspace approach requires Robin boundary conditions for the scalar field modes, the path integral approach requires adding an appropriate boundary term to the scalar field action, and the initial universe approach requires the initial quantum state of the scalar field to be Euclidean vacuum. We find that all three approaches yield identical wave functions and that scalar field fluctuations are well behaved, contrary to earlier claims in the literature.

@article{doi101103physrevd98066003,
    author = "Vilenkin, Alexander and Yamada, Masaki",
    title = "Tunneling wave function of the universe",
    year = "2018",
    journal = "Physical review. D/Physical review. D.",
    abstract = "The tunneling wave function of the universe is investigated in a minisuperspace framework of a de Sitter universe with a quantum scalar field, treated as a perturbation. We consider three different approaches to defining the tunneling wave function: (1) tunneling boundary conditions in superspace, (2) Lorentzian path integral, and (3) quantum tunneling from initial universe of a vanishing size. We show that the superspace approach requires Robin boundary conditions for the scalar field modes, the path integral approach requires adding an appropriate boundary term to the scalar field action, and the initial universe approach requires the initial quantum state of the scalar field to be Euclidean vacuum. We find that all three approaches yield identical wave functions and that scalar field fluctuations are well behaved, contrary to earlier claims in the literature.",
    url = "https://doi.org/10.1103/physrevd.98.066003",
    doi = "10.1103/physrevd.98.066003",
    openalex = "W2885315947",
    references = "doi101103physrevd502581"
}

Abstract The origin and evolution of the universe constitutes one of the most fascinating and challenging questions in the scientific investigation of nature. The general theory of relativity has made it possible to properly address this question. Einstein transformed cosmology when he formulated, in 1917, a relativistic model that could describe the universe in its entirety. The incorporation of the observational evidence of extragalactic recession into relativistic world models culminated in 1930 with the recognition of the expanding universe, which was a breakthrough in the scientific understanding of the universe as a whole. This chapter traces the history of the early phase of modern cosmology, from the formulation of the first cosmological models based on general relativity to the acceptance of the expanding universe and the early systematization of relativistic cosmology as a new scientific discipline.

@incollection{doi101093oxfordhb97801988176660133,
    author = "Realdi, Matteo",
    title = "Relativistic models and the expanding universe",
    year = "2019",
    booktitle = "Oxford University Press eBooks",
    abstract = "Abstract The origin and evolution of the universe constitutes one of the most fascinating and challenging questions in the scientific investigation of nature. The general theory of relativity has made it possible to properly address this question. Einstein transformed cosmology when he formulated, in 1917, a relativistic model that could describe the universe in its entirety. The incorporation of the observational evidence of extragalactic recession into relativistic world models culminated in 1930 with the recognition of the expanding universe, which was a breakthrough in the scientific understanding of the universe as a whole. This chapter traces the history of the early phase of modern cosmology, from the formulation of the first cosmological models based on general relativity to the acceptance of the expanding universe and the early systematization of relativistic cosmology as a new scientific discipline.",
    url = "https://doi.org/10.1093/oxfordhb/9780198817666.013.3",
    doi = "10.1093/oxfordhb/9780198817666.013.3",
    openalex = "W2965465277",
    references = "doi101007s1069901092183"
}

@incollection{doi10100797898115725318,
    author = "Meijer, Dirk K. F. and Jerman, Igor and Melkikh, Alexey V. and Sbitnev, Valeriy I.",
    title = "Biophysics of Consciousness: A Scale-Invariant Acoustic Information Code of a Superfluid Quantum Space Guides the Mental Attribute of the Universe",
    year = "2020",
    booktitle = "Studies in Rhythm Engineering",
    url = "https://doi.org/10.1007/978-981-15-7253-1\_8",
    doi = "10.1007/978-981-15-7253-1\_8",
    openalex = "W3095995742",
    references = "doi1010079783319050621, doi101016jbiosystems201310005"
}

HU is the Hypergeometrical Universe Theory (HU)[1-8], proposed in 2006, where the Universe is a Lightspeed Expanding Hyperspherical Hypersurface and Gravitation is an absolute-velocity-dependent, epoch-dependent force. Here we introduce the Big Pop Cosmogenesis and show our calculations associated with the Equation of State of the Universe. This article is the first in a series of articles[9-22] supporting the paradigm shift.

@misc{doi1020944preprints2022010106v1,
    author = "Pereira, Marco",
    title = "HU - The Big Pop Cosmogenesis Equation of State",
    year = "2022",
    booktitle = "Preprints.org",
    abstract = "HU is the Hypergeometrical Universe Theory (HU)[1-8], proposed in 2006, where the Universe is a Lightspeed Expanding Hyperspherical Hypersurface and Gravitation is an absolute-velocity-dependent, epoch-dependent force. Here we introduce the Big Pop Cosmogenesis and show our calculations associated with the Equation of State of the Universe. This article is the first in a series of articles[9-22] supporting the paradigm shift.",
    url = "https://doi.org/10.20944/preprints202201.0106.v1",
    doi = "10.20944/preprints202201.0106.v1",
    openalex = "W4205592212",
    references = "doi101007bf01397481, doi1010160031916364911369, doi10106311623617, doi101098rspa19210029, doi101103physrev1451156, doi101103physrevd23347, doi101103physrevlett114031103, doi101103physrevlett121261301, doi101103physrevlett13508, doi101142s0218271815300013, doi104172173643371000248, openalexw2953388962"
}