MG11 
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Abstract

de Sitter stability in theories with second order curvature terms

A general form of second order curvature corrections leads to forth-order equations of motion. This may cause some solution of unperturbed equations to be unstable. We derive conditions which ensure that de Sitter solution in General Relativity remains stable with respect to second order curvature terms.

Regular and chaotic dynamics of an FRW Universe with a scalar field

A transient chaos in a closed FRW cosmological model with a scalar field is studied. We describe two different chaotic regimes and show how the type of chaos depends on the scalar field potential. We also describe transition to a regular dynamics for steep potentials.

Cosmological dynamics with vacuum polarization

We consider de Sitter stability in modified gravity theories with respect to vacuum polarization. We assume that an analog of the Friedmann equation in the theory under consideration has the form $H=f(\rho)$, where $H$ is the Hubble parameter, $\rho$ is the matter density. After adding the vacuum polarization terms, this algebraic equation becomes a differential one. We write down eigenvalues of corresponding dynamical system in a de Sitter point, and show that stability of de Sitter solution depends on the sign of $df/d\rho$. A de Sitter point located at a phantom branch (where $df/d\rho < 0$) is unstable with respect to vacuum polarization.