Inflationary Cosmology in a non-minimal $f(R,T)$ gravity theory using a $RT$ mixing term

Abstract

We investigate a class of inflationary models in modified gravity theories which contain a non-minimal coupling between gravity and a scalar field $ϕ$ (inflaton) as $f(R,T)=R \bigl(1+α+ κ^4 βT \bigr)+κ^2γT $ where $κ^2=8πG$ where $G$ is the Newton's constant. We consider two inflaton potentials of the form (i) $V = V_0 \bigl(1 +\lnϕ \bigr)$ and (ii) $V_0\frac{λϕ^p}{1+λϕ^p}$. For a range of potential parameters, we explored the constraints on modified gravity parameters i.e. ($α$, $β$ and $γ$) in three categories -- (i) $β\neq0$, $α=γ=0$ (considering $R$ and $RT$ mixing terms), (ii) $α=0$, $γ\neq0$, $β\neq 0$ ($RT$ mixing term along with $T$ and $R$ terms) and (iii) $γ=0$, $α\neq0$, $β\neq0$ ($RT$ mixing term along with $R$ term) for the above two potentials. The inclusion of $RT$ mixing term provides the scalar spectral index $n_s$ up to $3σ$ limit of PLANCK data, which is $n_s=0.9649\pm0.0042$ as well as the tensor-to-scalar ratio $r<0.106$ and the e-fold parameter $40<N<70$ for both the potentials.