Physically constraining ℱ(R) corrected rainbow gravity through gravitational baryogenesis

This paper will discuss the gravitational baryogenesis mechanism with [Formula: see text] gravity, combined with rainbow gravity, in which higher-order curvature corrections and the dependence of energy on the spacetime metric are considered. Through the interaction between the derivative of the Ricci scalar and the baryon current in expanding Universe, the baryon asymmetry is produced by the CP-breaking interaction. The existence of rainbow functions changes the usual cosmological dynamics and causes a correction on the Friedmann equations, which consequently impact the development of the Ricci scalar throughout the radiation-dominated era. We investigate the possible forms of the function [Formula: see text], i.e. [Formula: see text] and [Formula: see text] and in the power-law solutions of the scale factor accordingly. With such solutions, we compute the decoupling temperature and the baryon-to-entropy ratio and put them as functions of the model parameters and rainbow functions. The ranges of the free parameters are imposed by imposing the observational limits on the baryon asymmetry. Compared with existing cosmological measurements, the integrated [Formula: see text] rainbow gravity model can easily give the required value of the baryon to entropy ratio without including other baryogenesis processes.