Homogeneous Solutions of Quadratic Gravity

TL;DR

This paper analyzes homogeneous solutions in quadratic gravity, focusing on Bianchi I models, to understand their dynamics and potential implications for early universe cosmology.

Contribution

It develops the 3+1 decomposition for homogeneous spaces in quadratic gravity and examines Bianchi I solutions, providing insights into their dynamics and relation to more general models.

Findings

3+1 decomposition for homogeneous spaces in quadratic gravity

Bianchi I solutions as a limiting case with negligible potential

Potential insights into general Bianchi models from Bianchi I analysis

Abstract

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. In this work we present the 3+1 decomposition for the zero vorticity case for arbitrary spatially homogenous spaces. We specialize for the particular Bianchi $I$ diagonal case. The 3- curvature can be understood as a generalized potential, and the Bianchi $I$ case is a limiting case where this potential is negligible to the dynamics. The spirit should be analogous, in some sense to the BKL solution. In this sense, a better understanding of the Bianchi $I$ case could shed some light into the general Bianchi case.