Constraints on the Combined Models with $R^{2-q}$ Inflation and Viable $f(R)$ Dark Energy

TL;DR

This paper constrains combined $R^{2-q}$ inflation and $f(R)$ dark energy models using Planck data, limiting deviation parameters and refining inflationary predictions.

Contribution

It provides observational bounds on the deviation parameter $q$ and $f(R)$ model parameters in combined inflation-dark energy scenarios.

Findings

$q < 2.66 imes 10^{-2}$ for power-law $f(R)$

$q < 2.17 imes 10^{-2}$ for exponential $f(R)$

Spectral index and tensor-to-scalar ratio are tightly constrained

Abstract

We investigate the observational constraints on the modified gravity, which combines the $R^{2-q}$ inflation with the power-law (exponential) type of the viable $f(R)$ dark energy models. We discuss the difference between the combined model and $R^{2-q}$ gravity in the inflationary epoch and obtain the constraints on the deviation power $q$ as well as the parameters in $f(R)$ by using the CosmoMC package. The allowed ranges of the spectral index and tensor-to-scalar ratio from the Planck data are highly restricted, resulting in $q < 2.66 \times 10^{-2}$ and $2.17 \times 10^{-2}$ for the power-law and exponential types of $f(R)$ gravity, respectively.