De Sitter Solutions in Models with the Gauss-Bonnet Term

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.