  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.
