Exact cosmological solutions of scale-invariant gravity theories

TL;DR

This paper derives new anisotropic vacuum solutions in scale-invariant gravity theories, extending Einstein's general relativity, and analyzes their properties, stability, and differences from classical Kasner solutions.

Contribution

It introduces exact anisotropic vacuum solutions in $R^{1+ ext{delta}}$ gravity, generalizing Kasner solutions and exploring their stability and physical implications.

Findings

Solutions exist for -1/2<delta<1/4

Solutions reduce to Kasner when delta=0

No chaotic Mixmaster oscillations for delta>0

Abstract

We have found new anisotropic vacuum solutions for the scale-invariant gravity theories which generalise Einstein's general relativity to a theory derived from the Lagrangian $R^{1+\delta}$. These solutions are expanding universes of Kasner form with an initial spacetime singularity at $t=0 $ and exist for $-1/2<\delta <1/4$ but possess different Kasner index relations to the classic Kasner solution of general relativity to which they reduce when $\delta =0$. These solutions are unperturbed by the introduction of non-comoving perfect-fluid matter motions if $p<\rho $ on approach to the singularity and should not exhibit an infinite sequence of chaotic Mixmaster oscillations when $\delta >0$.