Slow-roll inflation in f(R,T) gravity and a modified Starobinsky-like inflationary model

TL;DR

This paper explores slow-roll inflation within $f(R,T)$ gravity, analyzing various inflationary models and showing that the modified Starobinsky-like model aligns well with Planck data, offering flexible predictions for key inflation parameters.

Contribution

It introduces a framework for slow-roll inflation in $f(R,T)$ gravity and evaluates its implications for different inflationary potentials, including a modified Starobinsky model.

Findings

Starobinsky-like model predictions match Planck data for certain parameter ranges.

Modified natural and hilltop models show non-trivial parameter effects.

Wide range of $r$ and $n_T$ values are compatible with observations.

Abstract

In this work, we studied the slow-roll approximation of cosmic inflation within the context of $f(R,T)$ gravity, where $R$ is the scalar curvature, and $T$ is the trace of the energy-momentum tensor. By choosing a minimal coupling between matter and gravity, we obtained the modified slow-roll parameters, the scalar spectral index ($n_s$), the tensor spectral index ($n_{\textrm{T}}$), and the tensor-to-scalar ratio ($r$). We computed these quantities for a general power-law potential, Natural & Quartic Hilltop inflation, and the Starobinsky model, plotting the trajectories on the $(n_s,r)$ plane. We found that one of the parameters of Natural/Hilltop models is non-trivially modified. Besides, if the coupling is in the interval $-0.5 < \alpha < 5.54$, we concluded that the Starobinsky-like model predictions are in good agreement with the last Planck measurement, but with the advantage of allowing a wide range of admissible values for $r$ and $n_{\textrm{T}}$.