Observational Restrictions and Slow-Roll D-brane Inflation in the Special $F(\phi ,T)$ Gravity

We shall investigate the inflation for the D-brane model, motivated by the modified gravity $F(\phi ,T)$. This gravity has been recently introduced in the literature. The feasibility of the D-brane inflation theory in the $F(\phi ,T)$-gravity has been studied in conjunction with the most recent Planck data. We shall analyze the slow-roll inflation in the context of the $F(\phi )T$-gravity, via the D-brane model. Then, we shall calculate the inflation dynamics to obtain the scalar spectral index $n_s$'' and the tensor-to-scalar ratio $r$’'. Besides, we investigate the dynamics of the reheating for this model. Our model accurately covers the left-hand side of the Planck data and the D-brane inflation.