Inflationary Cosmology in a non-minimal $f(R,T)$ gravity theory using a $RT$ mixing term

We investigate a class of inflationary models in modified gravity theories which contain a non-minimal coupling between gravity and a scalar field $\phi$ (inflaton) as $f(R,T)=R(1+\alpha +{\kappa }^4\beta T)+{\kappa }^2\gamma T$ where ${\kappa }^2=8\pi G$ where $G$ is the Newton’s constant. We consider two inflaton potentials of the form (i) $V=V_0(1+\ln \phi )$ and (ii) $V_0\frac{\lambda {\phi }^p}{1+\lambda {\phi }^p}$. For a range of potential parameters, we explored the constraints on modified gravity parameters i.e. ($\alpha$, $\beta$ and $\gamma$) in three categories – (i) $\beta \mathrm{\ne }0$, $\alpha =\gamma =0$ (considering $R$ and $RT$ mixing terms), (ii) $\alpha =0$, $\gamma \mathrm{\ne }0$, $\beta \mathrm{\ne }0$ ($RT$ mixing term along with $T$ and $R$ terms) and (iii) $\gamma =0$, $\alpha \mathrm{\ne }0$, $\beta \mathrm{\ne }0$ ($RT$ mixing term along with $R$ term) for the above two potentials. The inclusion of $RT$ mixing term provides the scalar spectral index $n_s$ up to $3\sigma$ limit of PLANCK data, which is $n_s=0.9649\pm 0.0042$ as well as the tensor-to-scalar ratio $r<0.106$ and the e-fold parameter $40<N<70$ for both the potentials.