Abstract
In this paper we discuss models satisfying the limiting curvature condition. For this purpose we modify the Einstein-Hilbert action by adding a term which restricts the growth of curvature. We analyze cosmological solutions in such models. Namely, we consider a closed contracting homogeneous isotropic universe filled with thermal radiation. We demonstrate that for properly chosen curvature constraints such a universe has a bounce. As a result its evolution is nonsingular and contains a "de Sitter-type" supercritical stage connecting contracting and expanding phases. Possible generalizations of these results are briefly discussed.
Highlights
The idea that the Universe can have a prehistory before the big bang is very old
Cyclic or oscillating cosmological models were considered almost 90 years ago. Such models were discussed in the famous book by Tolman published in 1934 [1]. He demonstrated that the validity of the second law of thermodynamics applied to the Universe and increasing entropy make pure periodic models impossible: each of the successive cycles should be longer and larger than the previous one
Even if one does not require the existence of an infinite number of cycles before the formation of the present Universe, it is interesting to analyze an option that the Universe before the big bang had a phase of contraction, usually called a big crunch
Summary
The idea that the Universe can have a prehistory before the big bang is very old. Cyclic or oscillating cosmological models were considered almost 90 years ago. Markov [3,4] suggested that the existence of the limiting curvature should be considered as a new physical principle He demonstrated that for a proper choice of the equation of state in the cosmology the limiting curvature condition is satisfied and solutions in such a model describe a bouncing universe. In this paper we discuss bouncing cosmological models in a new recently proposed limiting curvature gravity (LCG) theory [21]. The main idea of this approach is to modify the Einstein-Hilbert action by adding a constraint term which controls the curvature behavior and forbids its infinite growth This is a realization of the Markov’s old idea about the existence of a limiting curvature. Some additional technical details and results used in the main text are collected in the Appendix
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