Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-06-02
Phys.Rev. D74 (2006) 083516
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Version accepted for publication in PRD. More references added, a few modifications and minor corrections
Scientific paper
10.1103/PhysRevD.74.083516
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 $\Lambda=0$, there are sets of initial conditions which form basins of attraction that asymptote Minkowski space. The complement of this set of initial conditions form basins which are attracted to some singular solutions. It is also shown, for a cosmological constant $\Lambda> 0$ that there are basins of attraction to a specific de Sitter solution. This result is consistent with Starobinsky's initial idea. The complement of this set also forms basins that are attracted to some type of singular solution. Because the singularity is characterized by curvature scalars, it must be stressed that the basin structure obtained is a topological invariant, i.e., coordinate independent.
Muller Daniel
Vitenti Sandro D. P.
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