Inflationary Cosmology in the Modified $f(R,T)$ Gravity

In this work, we study the inflationary cosmology in modified gravity theory $f(R,T)=R+2\lambda T$ ($\lambda$ is the modified gravity parameter) with three distinct class of inflation potentials (i) ${\phi }^p{e}^{-\alpha \phi }$, (ii) $(1-{\phi }^p)e^{-\alpha \phi }$ and (iii) $\frac{\alpha {\phi }^2}{1+\alpha {\phi }^2}$ where $\alpha$, $p$ are the potential parameters. We have derived the Einstein equation, potential slow-roll parameters, the scalar spectral index $n_s$, tensor to scalar ratio $r$, and tensor spectral index $n_T$ in modified gravity theory. We obtain the range of $\lambda$ using the spectral index constraints in the parameter space of the potentials. Comparing our results with PLANCK 2018 data and WMAP data, we found out the modified gravity parameter $\lambda$ lies between $-0.37<\lambda <1.483$.