Accelerated Expansion of the Universe in Gauss-Bonnet Gravity

TL;DR

This paper demonstrates that Gauss-Bonnet gravity with a negative coefficient can explain the universe's accelerated expansion without a cosmological constant, aligning with recent cosmological observations.

Contribution

It introduces a new solution in Gauss-Bonnet gravity that accounts for cosmic acceleration without a cosmological constant, extending brane-world models.

Findings

The solution generates a de Sitter spacetime in higher dimensions.

The brane exhibits accelerated expansion with negative deceleration.

Modified Friedmann equations match observational data.

Abstract

We show that in Gauss-Bonnet gravity with negative Gauss-Bonnet coefficient and without a cosmological constant, one can explain the acceleration of the expanding Universe. We first introduce a solution of the Gauss-Bonnet gravity with negative Gauss-Bonnet coefficient and no cosmological constant term in an empty $(n+1)$-dimensional bulk. This solution can generate a de Sitter spacetime with curvature $n(n+1)/\{(n-2)(n-3)|\alpha|\}$. We show that an $(n-1)$-dimensional brane embedded in this bulk can have an expanding feature with acceleration. We also considered a 4-dimensional brane world in a 5-dimensional empty space with zero cosmological constant and obtain the modified Friedmann equations. The solution of these modified equations in matter-dominated era presents an expanding Universe with negative deceleration and positive jerk which is consistent with the recent cosmological data. We also find that for this solution, the $"n"th$ derivative of the scale factor with respect to time can be expressed only in terms of Hubble and deceleration parameters.