Inflationary Cosmology with a scalar-curvature mixing term $\xi R
  \phi^2$
  We study the cosmological constraints on the non-minimal scalar-curvature
mixing $\xi R \phi^2$ in inflationary cosmology with a class of scalar field
inflaton potentials (i) $V = V_0 \phi^pe^{-\lambda\phi}$, (ii) $V = V_0 (1 -
\phi^{p})e^{-\lambda\phi}$ (iii) $V=V_0(1-\lambda\phi)^p$ and (iv)
$V=V_0\frac{\alpha\phi^2}{1+\alpha\phi^2}$. We obtain constraints on the
non-minimal coupling parameter $\xi$ for $\phi$ values of the potentials $V$
corresponding to potential parameters $\lambda,~p$ and $\alpha$ by comparing
these with the Planck+WMAP data on spectral index of curvature perturbations
generated during inflation. We find that in the parameters space all the above
listed potentials can generate the e-fold number $N=40-60$ necessary for any
successful inflation model. The scalar spectral index $n_s$ and the tensor to
scalar ratio $r$ are found to lie within $3\sigma$ C.L of Planck 2018 data for
the potentials (i) $V\propto \phi^pe^{\lambda\phi}$ with $\lambda=0, p=2$;
$\lambda=0.1, p=2,~4$; $ \lambda =0.01, p=2,~4$; (ii) $V\propto
(1-\phi^{p})e^{-\lambda\phi}$ for $\lambda =0.01, p=2,4$, (iii) $V\propto
(1-\lambda\phi)^p$ for $\lambda=\pm 1,p=\pm 2$. We also find that the potential
$V\propto \frac{\alpha\phi^2}{1+\alpha\phi^2}$ with $\alpha=1,2$ can produce
the $n_s$ and $r$ values which are consistent with the WMAP3 data.
