Starobinsky Model in Rainbow Gravity

TL;DR

This paper explores the Starobinsky inflation model within gravity's rainbow framework, deriving spectral predictions and constraining model parameters using Planck 2015 data.

Contribution

It introduces a novel approach by applying gravity's rainbow functions in a power-law form to the Starobinsky model of inflation.

Findings

Rainbow parameter constrained to be less than 6.0

Number of e-folds compatible with Planck data is 42 to 87

Spectral index and tensor-to-scalar ratio derived and compared with observations

Abstract

In this paper, we study the Starobinsky model of inflation in the context of gravity's rainbow theory. We propose that gravity rainbow functions can be 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 models with Planck 2015 data. We discover that in order to be consistent with Planck data up to $2\sigma$ C.L., the viable values of $N_{k}$ $e$-folds would satisfy $42\lesssim N_{k}\lesssim 87$ and the rainbow parameter $\lambda$ is nicely constrained to be $\lambda \lesssim6.0$.