Inflationary Cosmology with a scalar-curvature mixing term $\frac{1}{2} \xi R \phi^2$

We use the PLANCK 2018 and the WMAP data to constraint inflation models driven by a scalar field $\phi$ in the presence of the non-minimal scalar-curvature mixing term $\frac{1}{2}\xi R \phi^2$. We consider four distinct scalar field potentials $\phi^p e^{-\lambda\phi},~(1 - \phi^{p})e^{-\lambda\phi},~(1-\lambda\phi)^p$ and $\frac{\alpha\phi^2}{1+\alpha\phi^2}$ to study inflation in the non-minimal gravity theory. We calculate the potential slow-roll parameters, predict the scalar spectral index $n_s$, tensor-to-scalar ratio $r$, leading and higher order non-Gaussianity parameters ($f_{NL},~\tau_{NL}$ and $g_{NL}$) and the amplitude of the scalar spectrum $A_s$ in the parameter ($\lambda, p, \alpha$) space of the potentials corresponding to different values of the non-minimal coupling parameter $\xi$. We have compared our results with the ones existing in the literature, and this indicates the present status of non-minimal inflation after the release of the PLANCK 2018 data.