On gravitational baryogenesis in inflationary $f(R)$ Cosmologies

Abstract

The present study investigates the feasibility of generating the observed baryon-antibaryon asymmetry of the Universe $η$ by gravitational baryogenesis during the inflationary phase of two $f(R)$ modified theories of gravity: the widely used Starobinsky $f(R)=R+R^{2}/M^{2}$ model, and the recently proposed power-law model $f(R)=c_{1}R^{2+k/4}+c_{2}R+c_{3}$ of Odintsov and Oikonomou (2025). The present investigation is undertaken in the Einstein frame. The motion of the scalaron is studied for the slow roll inflationary era using analytic approximate solutions. Some of the expressions for the Starobinsky model were obtained first by Motohashi and Nishizawa (2012) but the expressions for the power-law model of Odintsov and Oikonomou and its generalization are new. Although the values of $η$ calculated for both models are quite close to the observed value, they are based upon several assumptions that qualify these results. Asymmetries generated before the end of inflation must be diluted, making agreement with observation difficult to achieve unless baryogenesis occurs at the end of the inflation era. The calculations also assume rapid thermalization of the plasma of the gravitationally produced particles, and that the interaction rate of the baryon-violating processes is greater than the expansion rate of the Universe until decoupling. The present calculations strongly violate these assumptions and would require significant variation of input parameters, which is excluded by CMB observations, to obtain agreement. A complete treatment of thermalization of the gravitationally produced plasma, baryon-number violating freeze-out, and entropy dilution is required to establish whether or not gravitational baryogenesis during slow-roll inflation is a viable mechanism for producing the observed baryon asymmetry of the Universe for these inflationary $f(R)$ cosmologies.