On stability of simplest nonsingular inflationary cosmological models within general relativity and gauge theories of gravity

In this paper we provide approximate analytical analysis of stability of nonsingular inflationary chaotic-type cosmological models. Initial conditions for nonsingular solutions at the bounce correspond to dominance of potential part of the energy density of the scalar field over its kinetic part both within general relativity and gauge theories of gravity. Moreover, scalar field at the bounce exceeds the planckian value and on expansion stage these models correspond to chaotic inflation. Such solutions can be well approximated by explicitly solvable model with constant effective potential (cosmological term) and massless scalar field during the bounce and on stages of quasi-exponential contraction and expansion. Perturbative analysis shows that nonsingular inflationary solutions are exponentially unstable during contraction stage. This result is compared with numerical calculations.