Anisotropy in constraint 4D Gauss-Bonnet gravity

TL;DR

This paper proposes a modified 4D Einstein-Gauss-Bonnet gravity theory with a Lagrange multiplier to enable anisotropic cosmological studies, revealing non-conservative behavior and faster matter density decay at high redshifts.

Contribution

Introduces a covariant 4D Einstein-Gauss-Bonnet model with a Lagrange multiplier, allowing analysis of anisotropic cosmologies and comparison with observational data.

Findings

Theory becomes non-conservative

Matter density declines faster at high redshifts

Equivalent to original theory in isotropic case

Abstract

Recently a new 4D Einstein-Gauss-Bonnet theory has been introduced \textbf{[Phys. Rev. Lett. 124 (2020) 081301]} with a serious debate that it does not possess a covariant equation of motion in $4D$. This feature, makes impossible to consider non-symetric space-times in this model, such as anisotropic cosmology. In this note, we will present a new proposal to make this happen, by introducing a Lagrange multiplier to the action which eliminates the higher dimensional term from the equation of motion. The theory has then a covariant $4D$ equation of motion which is useful to study the less symmetric metrics. On top of FRW universe, the constraint theory is equivalent to the original $4D$ Einstein-Gauss-Bonnet gravity. We will then consider the anisotropic cosmology of the model and compare the theory with observational data. We will see that the theory becomes non-conservative and the matter density abundance falls more rapidly at larger redshifts compared to the conservative matter sources.