Abstract
An extremely fast exponential expansion of the Universe is typical for the stable version of the inflationary model, based on the anomaly-induced action of gravity. The total amount of exponential e-folds could be very large, before the transition to the unstable version and the beginning of the Starobinsky inflation. Thus, the stable exponential expansion can be seen as a pre-inflationary semiclassical cosmological solution. We explore whether this stable phase could follow after the bounce, subsequent to the contraction of the Universe. Extending the previous consideration of the bounce, we explore both stable expansion and the bounce solutions in the models with non-zero cosmological constant and the presence of background radiation. The critical part of the analysis concerns stability for small perturbations of the Hubble parameter. It is shown that the stability is possible for the variations in the bounce region, but not in the sufficiently distant past in the contraction phase.
Highlights
The importance of singularities in general relativity is partially based on the fact that they are unavoidable [1,2,3,4] and, indicate to the limits of applicability of the theory
The common belief is that, by properly extending general relativity, one arrives at the singularity-free theory
The natural question is whether one can achieve the cosmological solutions with bounce with the minimal set of, or even without any, additional assumptions
Summary
The importance of singularities in general relativity is partially based on the fact that they are unavoidable [1,2,3,4] and, indicate to the limits of applicability of the theory. We extend the information about the bounce solution by including the large cosmological constant and the background radiation These aspects of the model are relevant because a huge cosmological constant may be generated in the UV by symmetry restoration, while an intensive creation of matter from the vacuum is expected in the region of bounce, when the Universe leaves the de Sitter-type contraction phase. We explore the stability of the approximately exponential expansion and contraction with respect to the small perturbations of the conformal factor of the metric Taken together, these new results extend our general understanding of the possibility of the bounce due to the semiclassical contributions to the gravitational action.
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