Effective Gravity and Homogeneous Solutions

TL;DR

This paper explores solutions to an effective higher-derivative gravity theory near singularities, focusing on vacuum homogeneous Bianchi models, revealing isotropization and singular behaviors depending on initial conditions.

Contribution

It provides new insights into the solution space of effective higher-derivative gravity for Bianchi I and VII_A models, extending understanding beyond linearized approaches.

Findings

Solutions exhibit isotropization depending on initial conditions.

Singular solutions occur based on initial conditions.

Analysis extends previous work on vacuum homogeneous models.

Abstract

Near the singularity, gravity should be modified to an effective theory, in the same sense as with the Euler-Heisenberg electrodynamics. This effective gravity surmounts to higher derivative theory, and as is well known, a much more reacher theory concerning the solution space. On the other hand, as a highly non linear theory, the understanding of this solution space must go beyond the linearized approach. In this talk we will present some results previously published by collaborators and myself, concerning solutions for vacuum spatially homogenous cases of Bianchi types $I$ and $VII_A$. These are the anisotropic generalizations of the cosmological spatially "flat", and "open" models respectively. The solutions present isotropisation in a weak sense depending on the initial condition. Also, depending on the initial condition, singular solutions are obtained.