Power-law solutions of the f(G) gravity model with electromagnetic and scalar field

Abstract

In this article, the Gauss-Bonnet model of gravity is investigated, the action of which includes the Gauss-Bonnet invariant, the Maxwell term  and the scalar field. The model is considered in a flat, isotropic and homogeneous Friedman-Robertson-Walker universe in four dimensions at the late stages of the Universe evolution. The Minkowski metric is used. For the researched model, a system of equations of motion and a solution with a scale factor with a power and modified power dependence on time are found. To find a solution, the method of variation was used. Similar solutions are obtained using the Euler-Poisson equation and the method of lowering the order of the derivative, followed by the usage of the Euler-Lagrange equation. The values of , energy density and isotropic pressure are obtained, the graphs of which correspond to modern cosmological data. In the course of the research, it turned out that for a scale factor with a power-law dependence on time within the framework of the researched model, the parameter of the equation of state is equal to the value obtained when solving a model with a modified power-law scale factor. The deceleration parameter is negative, which confirms the realism of the proposed model within the framework of an accelerated expanding universe. When considering the energy conditions, it turned out that the conditions are fulfilled in both models, but the SEC is not fulfilled. A comparison of the values of the energy conditions of the two models is shown.