Bianchi I spacetimes within 4D Einstein-Gauss-Bonnet scalar field theory

TL;DR

This paper studies the evolution of anisotropies in Bianchi I spacetimes within 4D Einstein-Gauss-Bonnet scalar field theory, revealing accelerating solutions, Kasner-like solutions, and a new splitting behavior of the background geometry.

Contribution

It provides the first detailed analysis of anisotropic Bianchi I solutions in 4D Einstein-Gauss-Bonnet scalar field theory, including new solution families and asymptotic behaviors.

Findings

Existence of accelerating solutions with scalar and Gauss-Bonnet scalar acting as a cosmological constant.

Recovery of isotropic, anisotropic, and Minkowski solutions.

Discovery of Kasner-like and splitting solutions in anisotropic cases.

Abstract

We investigate the evolution of anisotropies in Bianchi I spacetimes within the framework of the 4D Einstein-Gauss-Bonnet scalar field theory. The field equations are formulated using dimensionless variables, and the asymptotic dynamics are studied through a combination of analytical and numerical techniques. For the locally rotationally symmetric case, we analytically explore the stationary points of the field equations. The analysis reveals the existence of accelerating solutions in which the scalar field and the Gauss-Bonnet scalar effectively play the role of a cosmological constant. As a result, both anisotropic and isotropic expanding solutions are recovered, along with the Minkowski spacetime. No scaling solutions are supported by the gravitational model. For the general anisotropic Bianchi I geometry with three distinct scale factors, we find that a class of compactified Kasner-like solutions is obtained. In addition, a new family of solutions follows, describing a two-dimensional splitting of the background geometry. This behavior is similar to the previously observed pure Einstein-Gauss-Bonnet theory in higher-dimensional spacetimes.