A note on splitting solutions in $4+1$ dimensional quadratic gravity

TL;DR

This paper explores anisotropic vacuum solutions in 4+1 dimensional quadratic gravity, demonstrating a stable solution where an initially anisotropic universe evolves into a 3D isotropic space plus an extra dimension, supported by numerical analysis.

Contribution

It introduces a specific anisotropic vacuum solution in 4+1 quadratic gravity and analyzes its stability and basin of attraction.

Findings

The solution is stable for certain coupling constants.

An initially anisotropic universe can evolve into a 3D isotropic space plus an extra dimension.

The basin of attraction covers a significant portion of initial conditions.

Abstract

In the present paper we consider anisotropic cosmological vacuum solutions in (4+1) dimensional general quadratic gravity. In particular, we present a solution with 3 equal and 1 different Hubble parameters, and study its stability. We show that for a certain range of coupling constants this solution is stable. This means that initially totally anisotropic 4-dim Universe can evolve naturally to a product of 3-dim isotropic subspace and 1-dim space. By numerical integration of equations of motion we construct bassin of attraction of this solution which covers part of the initial conditions space with non-zero measure.