Modified gravity models for inflation with non-minimal coupling trace of energy-momentum tensor of the scalar field and Gauss-Bonnet invariant

Abstract

The article studies the inflationary properties of a cosmological model with the scalar field containing a non-minimal coupling with a modified Gauss-Bonnet invariant  \beta f(G)f(\varphi)   and the trace of the energy-momentum tensor of the scalar field \alpha f(\varphi) T in the framework of a flat, homogeneous and isotropic Friedman-Robertson-Walker Universe. To study the inflationary properties of the model, the chaotic potential, the natural potential, and the Starobinsky potential were selected. Within the framework of the slow-rolling approximation and assuming the coupling constants \alpha and \beta to be small ( \alpha<<1 and \beta<<1), generalized expressions for the scalar spectral index n_s and the scalar tensor ratio r are obtained. In the work, the Cobaya cosmology shell for cosmological calculations together with the Polychord sampler was used to calculate the theoretical values of the scalar spectral index and the scalar-tensor ratio and compare them with the observables. It is shown that for the chaotic potential, only the value of the scalar spectral index agrees with the observed data of Planck2018, and the value of the scalar-tensor ratio r exceeds the observed value. For the natural potential and the Starobinsky potential, both values of the inflationary parameters are consistent with observations. It is shown that for the case f(G)=G and all types of potentials, the coupling parameter \alpha  is marginalized in each model, and the coupling parameter \beta does not affect the dynamics of inflationary parameters and is not constrained in any way.