About Starobinsky inflation
Daniel Muller, Sandro D. P. Vitenti

TL;DR
This paper investigates numerical solutions in a higher derivative gravity theory inspired by Starobinsky inflation, revealing basins of attraction to Minkowski or de Sitter spaces and singular solutions, emphasizing the topological invariance of these structures.
Contribution
It provides a numerical analysis of anisotropic Bianchi I space-times in higher derivative gravity, demonstrating basin structures leading to different asymptotic states.
Findings
Basins of attraction to Minkowski space for zero cosmological constant
Basins of attraction to de Sitter space for positive cosmological constant
Basin structures are topologically invariant and coordinate independent
Abstract
It is believed that soon after the Planck era, space time should have a semi-classical nature. According to this, the escape from General Relativity theory is unavoidable. Two geometric counter-terms are needed to regularize the divergences which come from the expected value. These counter-terms are responsible for a higher derivative metric gravitation. Starobinsky idea was that these higher derivatives could mimic a cosmological constant. In this work it is considered numerical solutions for general Bianchi I anisotropic space-times in this higher derivative theory. The approach is ``experimental'' in the sense that there is no attempt to an analytical investigation of the results. It is shown that for zero cosmological constant , there are sets of initial conditions which form basins of attraction that asymptote Minkowski space. The complement of this set of initial…
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