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

In this work, we study the inflationary cosmology in modified gravity theory $f(R, T) = R + 2 λT$ ($λ$ is the modified gravity parameter) with three distinct class of inflation potentials (i) $ϕ^p e^{-αϕ}$, (ii) $(1-ϕ^p)e^{-αϕ}$ and (iii) $\frac{αϕ^2}{1+αϕ^2}$ where $α$, $p$ 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 $λ$ 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 $λ$ lies between $-0.37<λ<1.483$.

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