Constraining $f(R)$ model through spectral indices and reheating temperature

TL;DR

This paper examines an $f(R)$ gravity model for inflation, constraining its parameters using spectral indices and reheating temperature, and finds it consistent with observational data and frame equivalence near $\,\delta=1$.

Contribution

It introduces a specific $f(R)$ model and analyzes its viability for inflation using spectral indices and reheating temperature, demonstrating frame equivalence near $\,\delta=1$.

Findings

The model predicts $\,\delta$ close to 0.98.

Reheating temperature around $10^{17}$ GeV is consistent with observations.

Scalar spectral index and tensor-to-scalar ratio match Planck 2018 data.

Abstract

We investigate a form of $ f(R) = {R^{1+\delta}}/{R_c^{\delta}}$ and study the viability of the model for inflation in the Jordan and the Einstein frames. This model is further analysed by using the power spectrum indices of the inflation and the reheating temperature. During the inflationary evolution, the model predicts a value of $\delta$ parameter very close to one ($\delta=0.98$), while the reheating temperature $T_{re} \sim 10^{17}$ GeV at $\delta=0.98$ is consistent with the standard approach to inflation and observations. We calculate the slow roll parameters for the minimally coupled scalar field within the framework of our model. It is found that the values of the scalar spectral index and tensor-to-scalar ratio are very close to the recent observational data, including those released by Planck 2018. We also show that the Jordan and the Einstein frames are equivalent when $\delta \sim 1 $ by using the scalar spectral index, tensor-to-scalar ratio and reheating temperature.