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+α(R/M)n,f(R)=R+αR2+βR2log(R/M2) and the Einstein–Hu–Sawicki model with n,α,β 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.