In general quadratic gravity with alpha = -10 beta, Starobinsky inflation remains reachable from a nonzero band of initial conditions, though the basin shifts from expanding to contracting starts as shear increases.
Dynamical system approach to FRW models in higher-order gravity theories
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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.
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Initial conditions for Starobinsky inflation in general quadratic gravity
In general quadratic gravity with alpha = -10 beta, Starobinsky inflation remains reachable from a nonzero band of initial conditions, though the basin shifts from expanding to contracting starts as shear increases.