Inflationary Cosmology in the Modified $f(R, T)$ Gravity

TL;DR

This paper explores inflationary cosmology within a modified $f(R,T)$ gravity framework, analyzing specific potentials and deriving key inflationary parameters, then constraining the modified gravity parameter $\lambda$ using observational data.

Contribution

It introduces a detailed analysis of inflation in $f(R,T)$ gravity with new potential classes and derives observational constraints on the modified gravity parameter $\lambda$.

Findings

$\lambda$ constrained between -0.37 and 1.483 by observational data.

Derived slow-roll parameters and spectral indices in the modified gravity context.

Compatibility of modified gravity inflation models with PLANCK 2018 and WMAP data.

Abstract

In this work, we study the inflationary cosmology in modified gravity theory $f(R, T) = R + 2 \lambda T$ ($\lambda$ is the modified gravity parameter) with three distinct class of inflation potentials (i) $\phi^p e^{-\alpha\phi}$, (ii) $(1-\phi^p)e^{-\alpha\phi}$ and (iii) $\frac{\alpha\phi^2}{1+\alpha\phi^2}$ where $\alpha$, $p$ are the potential parameters. We have derived the Einstein equation, potential slow-roll parameters, the scalar spectral index $n_s$, tensor to scalar ratio $r$, and tensor spectral index $n_T$ in modified gravity theory. We obtain the range of $\lambda$ using the spectral index constraints in the parameter space of the potentials. Comparing our results with PLANCK 2018 data and WMAP data, we found out the modified gravity parameter $\lambda$ lies between $-0.37<\lambda<1.483$.