Non-Minimal Inflation with a scalar-curvature mixing term $\frac{1}{2} \xi R \phi^2$

Abstract

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 propose four scalar field potentials $\phi^p e^{-\lambda\phi},~(1 - \phi^{p})e^{-\lambda\phi},~(1-\lambda\phi)^p$ and $\frac{\alpha\phi^2}{1+\alpha\phi^2}$ in the non-minimal scenario. We calculate the slow-roll parameters and predict the scalar spectral index $n_s$, the tensor to scalar ratio $r$ and tensor spectral index $n_T$ in the parameters($\lambda, p, \alpha$) space of the potential. We compare our results with the PLANCK 2018 and WMAP data and found that the non-minimal parameter $\xi$ lies between $10^{-3} \sim 10^{-5}$.Comment: 17 pages, 7 figures, 6 table