De Sitter Solutions in Models with the Gauss-Bonnet Term

Sergey Vernov,Ekaterina Pozdeeva

doi:10.3390/ecu2021-09305

Abstract

De Sitter solutions play an important role in cosmology because the knowledge of unstable de Sitter solutions can be useful in describing inflation, whereas stable de Sitter solutions are often used in models of the late-time acceleration of the Universe. Einstein–Gauss–Bonnet models are actively used as both inflationary models and dark energy models. To modify the Einstein equations, one can add a nonlinear function of the Gauss–Bonnet term or a function of the scalar field multiplied on the Gauss–Bonnet term. The effective potential method essentially simplifies the search and stability analysis of de Sitter solutions, because the stable de Sitter solutions correspond to the minima of the effective potential.

Highlights

We show that the effective potential proposed [31] for model with the Gauss–Bonnet term, multiplied on a function of the scalar field, can be used in W (G)
To find de Sitter solutions in a W (G) model, we rewrite the action of this model in the form (3) and construct the corresponding effective potential Ve f f
A stable de Sitter solution corresponds to Ve00f f > 0, where the values of the scalar field at the de Sitter point φdS are determined by the condition Ve0 f f = 0

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The current dark energy dominated epoch [5,6,7,25,26,27,28,29,30] Note that these studies of the Universe’s evolution are characterized by the quasi de Sitter accelerated expansion of the Universe. Gauss–Bonnet model with the standard scalar field, such a method has been proposed in [31]. This is a generalization of the effective potential method [32,33]. We generalize this method on a model with nonlinear functions of the Gauss–Bonnet term. We consider the case of a phantom scalar field and show that, in this case, the situation is more difficult

Models the Gauss-Bonnet Term

Stability of de Sitter Solutions

Conclusions