Some Cosmological Solutions in an Arbitrary Order of Lovelock Gravity

TL;DR

This paper explores cosmological solutions in Lovelock gravity, demonstrating the possibility of non-isotropizing solutions with matter and generalizing known solutions to arbitrary orders, including new anisotropic exponential solutions.

Contribution

It generalizes the Jacobs solution to any order of Lovelock gravity and finds a new anisotropic exponential solution at third order.

Findings

Cosmological solutions without isotropization are possible with matter.

The Jacobs solution is extended to arbitrary Lovelock orders.

A new anisotropic exponential solution is discovered at third order.

Abstract

We consider the Lovelock theory of gravity that assumes a nonlinearity of the field equations in the second-order derivatives of the metric. We prove the opportunity of obtaining cosmological solutions without isotropization in the presence of matter in the form of a perfect fluid, which is necessary for invisibility of extra dimensions that inevitably emerge in the Lovelock theory. In particular, the Jacobs solution has been generalized to an arbitrary order of the theory, and in the third order, an anisotropic exponential solution has been found.