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

Abstract

We use the PLANCK 2018 and the WMAP data to constraint inflation models driven by a scalar field $\varphi$ in the presence of the non-minimal scalar-curvature mixing term $\frac{1}{2}\xi R{\varphi }^2$. We consider four distinct scalar field potentials ${\varphi }^p{e}^{-\lambda \varphi },(1-{\varphi }^p)e^{-\lambda \varphi },(1-\lambda \varphi {)}^p$ and $\frac{\alpha {\varphi }^2}{1+\alpha {\varphi }^2}$ to study inflation in the non-minimal gravity theory. We calculate the potential slow-roll parameters and predict the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$, in the parameters ($\lambda ,p,\alpha$) space of the potentials. 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.

Comments: 19 pages, 3 figures, 6 tables