Modified FRW cosmology with massive gravity in the spectrum of the rainbow

In this study, authors investigate a novel framework incorporating exponential electrodynamics and d-dimensional energy-dependent massive gravity. Our focus lies in demonstrating that a nonlinear electromagnetic field, acting as the gravitational source, leads to an accelerated expansion of the universe. Employing massive gravity's rainbow as a catalyst for cosmic evolution, the big bang singularity inherent in the model is successfully eliminated. This analysis reveals that the synergy between the magnetic universe and massive gravity's rainbow is the underlying cause of the observed accelerated cosmic expansion. The classical stability during the deceleration phase and ensure the causality of the model are established. Additionally, we delve into 4-dimensional energy-dependent cosmology. Furthermore, approximations for key cosmological parameters such as the running of the spectral index, tensor-to-scalar ratio, and, the spectral index are presented. These estimations closely align with observational data from PLANCK and WMAP, providing valuable insights into the compatibility of the proposed model with empirical evidence.