The Early and Late Universe in the Modified Einstein-Maxwell-Gauss-Bonnet Model

Abstract

This work investigates the Einstein-Gauss-Bonnet model with scalar and electromagnetic fields. The created model was reconstructed using a hybrid scale factor. The initial viability analysis of the model confirmed the compliance of the solutions with modern cosmological data. The equation of state parameter $\omega$, corresponds to the case of an accelerated expanding universe. In addition, an alternative approach utilizing $Om(z)$ diagnostics has been implemented. The values of the scalar field and its potential obtained during the solution correspond to the cases of "slow-roll" and chaotic inflation. The values of the slow-roll parameters, based on the coupling function $\xi(\phi)$ are obtained. Parameters correspond to the condition of the beginning of inflation. Based on the slow-roll parameters, the values of the spectral indices $n_S$, $n_T$, and the tensor-to-scalar ratio $r$ are obtained. The propagation speed of the acoustic ($c_A$) and tensor ($c_T$) perturbations have been determined. Subsequently, an examination of the post-inflationary phase in the universe's evolution was conducted. This analysis was predicated on the utilization of energy conditions. Furthermore, an extensive evaluation involving cosmographic parameters and statefinders diagnostics was executed. The application of the described methods has shown that the model is stable, viable, and can be used to study the early and late stages of the universe's evolution.