Gauss-Bonnet Gravity in $D=4$ Without Gauss-Bonnet Coupling to Matter - Cosmological Implications

TL;DR

This paper introduces a novel D=4 Gauss-Bonnet gravity model using non-Riemannian volume elements, leading to unique cosmological solutions with implications for dark energy and universe evolution.

Contribution

It develops a new D=4 Gauss-Bonnet gravity framework that is non-trivial without matter coupling, revealing cosmological solutions with a dynamically generated integration constant.

Findings

Predicts matter-independent cosmological solutions

Provides a model for dark energy from geometric origins

Offers explicit analytic solutions for Friedmann equations

Abstract

We propose a new model of $D=4$ Gauss-Bonnet gravity. To avoid the usual property of the integral over the standard $D=4$ Gauss-Bonnet scalar becoming a total derivative term, we employ the formalism of metric-independent non-Riemannian spacetime volume elements which makes the D=4 Gauss-Bonnet action term non-trivial without the need to couple it to matter fields unlike the case of ordinary D=4 Gauss-Bonnet gravity models. The non-Riemannian volume element dynamically triggers the Gauss-Bonnet scalar to be an arbitrary integration constant M on-shell, which in turn has several interesting cosmological implications: (i) It yields specific solutions for the Hubble parameter and the Friedmann scale factor as functions of time, which are completely independent of the matter dynamics, i.e., there is no back reaction by matter on the cosmological metric; (ii) For M>0 it predicts a "coasting"-like evolution immediately after the Big Bang, and it yields a late universe with dynamically produced dark energy density given through M; (iii) For the special value M=0 we obtain exactly a linear "coasting" cosmology; (iv) For M<0 we have in addition to the Big Bang also a Big Crunch with "coasting"-like evolution around both; (v) It allows for an explicit analytic solution of the pertinent Friedmann and scalar field equations of motion, while dynamically fixing uniquely the functional dependence of the scalar potential.