Non-minimal RT coupling and its impact on inflationary evolution in f(R,T) gravity

Abstract

We examine inflationary models in the $f(R,T)$ gravity framework where we have a conformal constant and an RT-mixing term apart from an R term. The RT-mixing term introduces non-minimal coupling between gravity and matter. We consider the exponential SUSY potential $V\left(\varphi \right)=M^4(1-e^{-\lambda \varphi /M_{pl}})$ and a novel potential $V\left(\varphi \right)=\lambda M_{pl}^{4-2\alpha }{\varphi }^{2\alpha }{\sin }^2\left(\frac{\beta M_{pl}^{\alpha }}{{\varphi }^{\alpha }}\right)$. With the help of COBE normalization, we constrain values of different parameters and extract the field value at the time of Hubble crossing. The end of inflation is marked by ${\widetilde{ϵ}}_v\left({\varphi }_i\right)=1$ where ${\varphi }_i$ is the field value at the end of inflation. Equipped with these values, we then move on to calculate values of spectral index $n_s$ and tensor-to-scalar ratio r. Our predicted values of $n_s$ and r fall within their observed values from the Planck 2018 survey and BICEP/Keck array measurement for both potential, making them plausible candidates for the inflationary model. We also display the variation of the tensor-to-scalar ratio and spectral index with the coefficient of RT-mixing term for fixed values of e-fold number. There, we find the existence of two local maxima of $n_s$, which occur at a negative and a positive value of ξ, the coefficient of RT-mixing term. Our analysis finds a significant impact of ξ on values of observables.