Dynamical system approach to FRW models in higher-order gravity theories

Abstract

We study the late time evolution of positively curved FRW models with a scalar field which arises in the conformal frame of the $R+\alpha R^2$ theory. The resulted three-dimensional dynamical system has two equilibrium solutions corresponding to a de Sitter space and an ever expanding closed universe. We analyze the structure of the first equilibrium with the methods of the center manifold theory and, for the second equilibrium we apply the normal form theory to obtain a simplified system, which we analyze with special phase plane methods. It is shown that an initially expanding closed FRW spacetime avoids recollapse.

3 figures, to appear in JMP

References in corpus (1)

• Scalar-field cosmologies with an arbitrary potential

Cited by in corpus (15)

• Dynamical systems applied to cosmology: dark energy and modified gravity
• On dynamical systems approaches and methods in $f(R)$ cosmology
• Anisotropic cosmological solutions in $R+R^2$ gravity
• Energy exchange for homogeneous and isotropic universes with a scalar field coupled to matter
• Generality of Starobinsky and Higgs inflation in the Jordan frame
• The recollapse problem of closed FRW models in higher-order gravity theories
• The initial state of generalized radiation universes
• Slice Energy in Higher Order Gravity Theories and Conformal Transformations
• On stability of the Kasner solution in quadratic gravity
• Genericity of blackhole formation in the gravitational collapse of homogeneous self-interacting scalar fields
• The dynamical behaviour of homogeneous scalar-field spacetimes with general self-interaction potentials
• Gravitational collapse of homogeneous perfect fluid in HOG theories
• Dynamical stability of Minkowski space in higher order gravity
• Global models of collapsing scalar field: endstate
• Gravitational collapse of a spherical scalar field