Inflation from $f(R)$ theories in gravity's rainbow

TL;DR

This paper investigates inflationary models based on $f(R)$ gravity within gravity's rainbow framework, deriving spectral indices and tensor-to-scalar ratios, and finds that these models align well with Planck 2018 observational data.

Contribution

It introduces $f(R)$ inflationary models in gravity's rainbow, deriving key perturbation parameters and demonstrating their consistency with recent cosmological observations.

Findings

All models agree with Planck 2018 data for suitable parameters.

Derived spectral index and tensor-to-scalar ratio match observations.

Models can produce sufficient e-foldings with proper parameter choices.

Abstract

In this work, we study the $f(R)$ models of inflation in the context of gravity's rainbow theory. We choose three types of $f(R)$ models: $f(R)=R+\alpha (R/M)^{n},\,f(R)=R+\alpha R^{2}+\beta R^{2}\log(R/M^{2})$ and the Einstein-Hu-Sawicki model with $n,\,\alpha,\,\beta$ being arbitrary real constants. Here $R$ and $M$ are the Ricci scalar and mass scale, respectively. For all models, the rainbow function is written in the power-law form of the Hubble parameter. We present a detailed derivation of the spectral index of curvature perturbation and the tensor-to-scalar ratio and compare the predictions of our results with the latest Planck 2018 data. With the sizeable number of e-foldings and proper choices of parameters, we discover that the predictions of all $f(R)$ models present in this work are in excellent agreement with the Planck analysis.