# Deformed Starobinsky model in gravity's rainbow

## TL;DR

This paper explores a modified Starobinsky inflation model within gravity's rainbow framework, showing it aligns well with Planck data and constrains rainbow and model parameters.

## Contribution

It introduces a deformed $f(R)$ gravity model in gravity's rainbow and derives its inflationary predictions, matching observational data and constraining key parameters.

## Key findings

- Model predictions agree with Planck data for suitable parameters.
- Derived bounds on rainbow parameter $\, extlambda$ and deformation parameter $\, extalpha$.
- Expressed spectral index and tensor-to-scalar ratio in terms of model parameters.

## Abstract

In the context of gravity's rainbow, we study the deformed Starobinsky model in which the deformations take the form $f(R)\sim R^{2(1-\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter. We show that the spectral index of curvature perturbation and the tensor-to-scalar ratio can be written in terms of $N,\,\lambda$ and $\alpha$, with $N$ being the number of {\it e}-foldings, $\lambda$ a rainbow parameter. We compare the predictions of our models with Planck data. With the sizeable number of {\it e}-foldings and proper choices of parameters, we discover that the predictions of the model are in excellent agreement with the Planck analysis. Interestingly, we obtain the upper limit and the lower limit of a rainbow parameter $\lambda$ and a positive constant $\alpha$, respectively.