Geodesically complete analytic solutions for a cyclic universe

Bars, Itzhak; Chen, Shih-Hung; Turok, Neil

doi:10.1103/physrevd.84.083513

Cited by 52 publications

(77 citation statements)

References 33 publications

(158 reference statements)

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“…Our goal in this paper is to provide a full set of analytic solutions that give all possible configurations of a homogeneous and isotropic universe as a function of time. This expands on our previous work in [13][14][15] by including additional degrees of freedom, in particular radiation. The effects of anisotropy are discussed elsewhere [16,17].…”

Section: Introductionmentioning

confidence: 52%

“…The method, which is based on conformal symmetry, was introduced in previous papers [13]- [17]. It was applied to the cases of the flat and curved isotropic Friedmann universes without radiation or matter [14]. It was also applied to the case of an anisotropic universe in the absence of the potential energy, but with the inclusion of radiation [17].…”

Section: Introductionmentioning

confidence: 99%

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Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

et al. 2012

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We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters.Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null energy condition. There is a special subset of geodesically complete non-generic solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine tuning initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained. 98.80.Cq,

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Section: Introductionmentioning

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

et al. 2012

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“…II D, with limited success. An intriguing proposal by Bars et al in [55][56][57][58][59][60][61] allows to trace the evolution of the universe unambiguously through a singular bounce via a brief antigravity phase, see Sec. II E; however, a computation of observables in this framework has not been performed yet.…”

Section: B What Is Used To Get a Bounce?mentioning

confidence: 99%

“…In a series of papers, Bars et al [55][56][57][58][59][60][61] showed that theories motivated by the minimal conformal extension of the standard model with scalar fields coupled to gravity can be lifted to a Weyl-invariant theory that allows the cosmological evolution to be unambiguously traced through a big-crunch/big-bang (singular) transition. Here the classical evolution can be followed in a homogeneous, but potentially anisotropic (e.g.…”

Section: E Antigravitymentioning

confidence: 99%

A critical review of classical bouncing cosmologies

2015

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Given the proliferation of bouncing models in recent years, we gather and critically assess these proposals in a comprehensive review. The PLANCK data shows an unmistakably red, quasi scaleinvariant, purely adiabatic primordial power spectrum and no primary non-Gaussianities. While these observations are consistent with inflationary predictions, bouncing cosmologies aspire to provide an alternative framework to explain them. Such models face many problems, both of the purely theoretical kind, such as the necessity of violating the NEC and instabilities, and at the cosmological application level, as exemplified by the possible presence of shear. We provide a pedagogical introduction to these problems and also assess the fitness of different proposals with respect to the data. For example, many models predict a slightly blue spectrum and must be fine-tuned to generate a red spectral index; as a side effect, large non-Gaussianities often result.We highlight several promising attempts to violate the NEC without introducing dangerous instabilities at the classical and/or quantum level. If primordial gravitational waves are observed, certain bouncing cosmologies, such as the cyclic scenario, are in trouble, while others remain valid. We conclude that, while most bouncing cosmologies are far from providing an alternative to the inflationary paradigm, a handful of interesting proposals have surfaced, which warrant further research. The constraints and lessons learned as laid out in this review might guide future research.

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“…Note that the interest to the study of the possibility of crossing of such singularities is growing and some models treating this phenomenon have been elaborated during last few years [45].…”

Section: Discussionmentioning

confidence: 99%

Classical and quantum Big Brake cosmology for scalar field and tachyonic models

Kamenshchik¹,

Manti²

2013

AIP Conference Proceedings

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We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularitythe model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical -quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.

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Geodesically complete analytic solutions for a cyclic universe

Cited by 52 publications

References 33 publications

Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

A critical review of classical bouncing cosmologies

Classical and quantum Big Brake cosmology for scalar field and tachyonic models

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