Gravitational baryogenesis in $F(R)$ gravity's rainbow

We investigate the gravitational baryogenesis scenario within the context of $F(R)$ gravity's rainbow which incorporates both modified gravity and energy-dependent spacetime. This study explores a mechanism for generating baryon asymmetry based on the interaction between the derivative of the Ricci scalar $R$ and the baryon current within the framework of $F(R)$ gravity's rainbow. The rainbow functions, arising from quantum gravity effects, modify the gravitational interaction and the Friedmann equations, leading to a distinct evolution of the baryon asymmetry compared to standard $F(R)$ gravity. We analyze the conditions under which a viable baryon asymmetry can be produced, taking into account the constraints from cosmological observations and the specific form of the $F(R)$ function. By examining the cosmological equations in the context of $F(R)$ gravity's rainbow, we obtain power-law solutions for these equations. We also identify the decoupling temperature and the ratio of baryonic number to entropy density in this model, depending on the model's parameters. First, we discuss the acceptable intervals of the model's parameters which are defined by constraints on the background quantity. We note that the decoupling temperature and the ratio of baryon-to-entropy in these models depend on the value of the rainbow function. We compare the predictions of this model with the existing observational data. Our results suggest that $F(R)$ gravity's rainbow provides a novel mechanism for gravitational baryogenesis, potentially explaining the observed baryon asymmetry in the universe while incorporating quantum gravity corrections.