The dynamics of the flat anisotropic models in the Lovelock gravity. I: The even-dimensional case

TL;DR

This paper provides a comprehensive numerical and analytical study of the dynamics of flat anisotropic (4+1)-dimensional cosmological models in Lovelock gravity, including Gauss-Bonnet and Einstein terms, with and without matter.

Contribution

It offers the first complete description of this model with both Gauss-Bonnet and Einstein contributions, analyzing vacuum and matter-influenced regimes and their generalization to higher-order Lovelock models.

Findings

Matter smooths the transition between singularity and Kasner regimes.

Presence of matter introduces new regimes and blurs boundaries between regimes.

Numerical and analytical methods are used to explore higher-dimensional Lovelock models.

Abstract

In this article we give a full description of the dynamics of the flat anisotropic (4+1)-dimensional cosmological model in the presence of both Gauss-Bonnet and Einstein contributions. This is the first complete description of this model with both terms taken into account. Our data is obtained using the numerical analysis, though, we use analytics to explain some features of the results obtained, and the same analytics could be applied to higher-dimensional models in higher-order Lovelock corrections. Firstly, we investigate the vacuum model and give a description of all regimes; then, we add a matter source in the form of perfect fluid and study the influence the matter exerts upon the dynamics. Thus, we give a description of matter regimes as well. Additionally, we demonstrate that the presence of matter not only "improves" the situation with a smooth transition between the standard singularity and the Kasner regime, but also brings additional regimes and even partially "erases" the boundaries between different regimes inside the same triplet. Finally, we discuss the numerical and analytical results obtained and their generalization to the higher-order models.