Revisiting $f(R)$ gravity's rainbow: Inflation and primordial fluctuations

TL;DR

This paper explores inflation and primordial fluctuations within $f(R)$ gravity's rainbow, deriving power spectra and comparing predictions with observational data to constrain model parameters and rainbow functions.

Contribution

It introduces novel calculations of scalar and tensor spectra in $f(R)$ gravity's rainbow and provides new observational constraints on the model.

Findings

New predictions for scalar spectral index $n_s$ and tensor-to-scalar ratio $r$

Constraints on rainbow functions from observational data

Compatibility of the model with PLANCK and BICEP/Keck results

Abstract

We study inflation and the generation of primordial fluctuations in $f(R)$ gravity's rainbow. We calculate the cosmological perturbations and then the scalar and tensor primordial power spectrum. We contrast the predictions of the model with the current observational data from PLANCK and BICEP/Keck. Particularly, we found new results for the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ along with new observational constraints on the rainbow functions.