Interacting F(R, T) gravity with modified Chaplygin gas

In this paper, we have studied F(R, T) gravity as an arbitrary function of curvature and torsion scalars in Friedmann- Lemaitre-Robertson-Walker background. Then, we have considered interacting model between F(R, T) gravity and modified Chaplygin gas. The novelty of this model is that the Universe includes both curvature and torsion cases, and one dominated by a Chaplygin gas. To calculate cosmological solutions, we obtained the Friedmann equations and also equation of state parameter of dark energy. By employing the interacting model we considered the total energy density and the total pressure of the Universe as the combination of components of dark energy and Chaplygin gas. Subsequently, we reconstructed the model by an origin of a scalar field entitled quintessence model with a field potential. The field potential has been calculated in terms of free parameters of F(R, T) gravity and modified Chaplygin gas. In what follows, we used a parametrization, and the cosmological parameters have been written in terms of redshift z. Next, we plotted cosmological parameters with respect to three variables: cosmic time, redshift z, and e-folding number N = ln(a), and the figures showed us an accelerated expansion of the Universe. Also, we have described the scenario in three statuses: early time, late time, and future time, by e-folding number. Finally, the stability of the scenario has been investigated using sound speed, and the graph of sound speed versus e-folding number has shown us that there is stability in late time. (author)