On the no-boundary proposal for ekpyrotic and cyclic cosmologies

Battarra, Lorenzo; Lehners, Jean-Luc

doi:10.1088/1475-7516/2014/12/023

Cited by 40 publications

(52 citation statements)

References 56 publications

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“…The spectrum of curvature fluctuations in the old ekpyrotic scenario was found to be deeply blue [134][135][136][137] (an additional problem is that these modes do not become classical [138] as opposed to the ones resulting from the entropic mechanism [139] described below). As a result, two-field models [140] were introduced to overcome this problem [141][142][143][144].…”

Section: B Ekpyrotic and Cyclic Scenariosmentioning

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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Section: B Ekpyrotic and Cyclic Scenariosmentioning

confidence: 99%

A critical review of classical bouncing cosmologies

2015

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“…By multiplying (27) through by q 2 and solving near q = 0 one can immediately see that a regular solution requires U ,β ± = 0 at q = 0, which, if we assume that the saddle point will still be the Hartle-Hawking one with q(t = 0) = 0, translates into the requirement β ± (0) = 0. This is indeed a Dirichlet condition, which moreover ensures that the constraint (28) can also be satisfied at the South Pole.…”

Section: The Simplest Case: the "No Boundary Term" Proposalmentioning

confidence: 99%

No-boundary prescriptions in Lorentzian quantum cosmology

2019

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We analyse the impact of various boundary conditions on the (minisuperspace) Lorentzian gravitational path integral. In particular we assess the implications for the Hartle-Hawking no-boundary wavefunction. It was shown recently that when this proposal is defined as a sum over compact metrics, problems arise with the stability of fluctuations. These difficulties can be overcome by an especially simple implementation of the no-boundary idea: namely to take the Einstein-Hilbert action at face value while adding no boundary term. This prescription simultaneously imposes an initial Neumann boundary condition for the scale factor of the universe and, for a Bianchi IX spacetime, Dirichlet conditions for the anisotropies. Another way to implement the no-boundary wavefunction is to use Robin boundary conditions. A sub-class of Robin conditions allows one to specify the Hubble rate on the boundary hypersurface, and we highlight the surprising aspect that specifying the final Hubble rate (rather than the final size of the universe) significantly alters the off-shell structure of the path integral. The conclusion of our investigations is that all current working examples of the no-boundary wavefunction force one to abandon the notion of a sum over compact and regular geometries, and point to the importance of an initial Euclidean momentum.

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“…The first three equations yield the generalized momenta, while Eqns. (23), (24) are the Friedmann equations of F(R) gravity in the holonomy corrected scenario, and Eqn. (25) is the conservation equation of the scalar field.…”

Section: B Holonomy Improvementmentioning

confidence: 99%

Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier

2020

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Matter and quasi-matter bounce scenarios are studied for an F(R) gravity model with holonomy corrections and a Lagrange multiplier, with a scale factor a(t) = a0t 2 + 1 n , where the Hubble parameter squared has a linear and a quadratic dependence on the effective energy density. Provided n < 1/2, it is shown that the primordial curvature perturbations are generated deeply into the contracting era, at large negative time, which makes the low-curvature limit a good approximation for calculating the perturbation power spectrum. Moreover, it is shown that, for n within this range, the obtained cosmological quantities are fully compatible with the Planck constraints, and that the "low curvature limit" comes as a viable approximation to calculate the power spectra of both scalar and tensor perturbations. Using reconstruction techniques for F(R) gravity with the Lagrange multiplier, the precise form of the effective F(R) gravity is found, from which one determines the power spectra of scalar and tensor perturbations in such bouncing scenario. Correspondingly, the spectral index for curvature perturbations and the tensor to scalar ratio are obtained, and these values are successfully confronted with the latest Planck observations. Further, it is shown that both the weak and the null energy conditions are satisfied, thanks to the holonomy corrections performed in the theory-which are then proven to be necessary for achieving this goal. In fact, when approaching the bouncing era, the holonomy corrections become significant and play a crucial role in order to restore the energy conditions. Summing up, a cosmological bouncing scenario with the scale factor above and fulfilling the energy conditions can be adequately described by the F(R) model with a Lagrange multiplier and holonomy corrections, which prove to be very important.

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On the no-boundary proposal for ekpyrotic and cyclic cosmologies

Cited by 40 publications

References 56 publications

A critical review of classical bouncing cosmologies

A critical review of classical bouncing cosmologies

No-boundary prescriptions in Lorentzian quantum cosmology

Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier

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