Dark equation of state for the Gauss–Bonnet universe

Abstract

We study pressure models in higher dimensional general relativity and Einstein-Gauss–Bonnet (EGB) gravity in a spherically symmetric spacetime. In EGB gravity, we show that the dynamics of the model are governed by an Abel differential equation of the second kind. A general first integral is possible for all values of the spatial curvature, equation of state parameter and spacetime dimension. We further show that an explicit solution is possible for the cosmic scale factor in EGB gravity for the dark energy equation of state. We further demonstrate that for the dark energy equation of state, an anti-de Sitter-Gauss–Bonnet universe is possible, which is not necessarily the case in general relativity. It is also shown that the effective pressure of the Gauss–Bonnet universe contains the higher order curvature corrections and remains, like the general relativity case, negative for all dimensions. The Hawking temperature of the dark Gauss–Bonnet universe is found and is positive and constant for all spatial curvature, and depends critically on the spacetime dimension.