(Not so) pure Lovelock Kasner metrics

TL;DR

This paper reviews pure Lovelock gravity equations for Kasner metrics, focusing on their behavior near the big-bang singularity and classifying solutions based on isotropy types, highlighting degeneracies and subleading effects.

Contribution

It provides a classification of pure Lovelock Kasner solutions and discusses their degeneracies and sensitivity to subleading terms in higher curvature gravity theories.

Findings

Classified Kasner solutions into isotropy types.

Identified degenerate solution classes sensitive to subleading terms.

Highlighted relevance to early universe singularity dynamics.

Abstract

The gravitational interaction is expected to be modified for very short distances. This is particularly important in situations in which the curvature of spacetime is large in general, such as close to the initial cosmological singularity. The gravitational dynamics is then captured by the higher curvature terms in the action, making it difficult to reliably extrapolate any prediction of general relativity. In this note we review pure Lovelock equations for Kasner-type metrics. These equations correspond to a single $N$th order Lovelock term in the action in $d=2N+1,\,2N+2$ dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. These are classified in several isotropy types. Some of these families correspond to degenerate classes of solutions, such that their dynamics is not completely determined by the equations of pure Lovelock gravity. Instead, these Kasner solutions become sensitive to the subleading terms in the Lovelock series.