Baryon asymmetry from higher-order matter contributions in gravity

We investigate the observed asymmetry between matter and antimatter by incorporating higher-order matter contributions in gravity, specifically analyzing gravitational baryogenesis within the framework of $f(R,T^2)$ gravity, where R is the Ricci scalar and $T^2\equiv T_{\mu \nu }{T}^{\mu \nu }$. We further explore the impact of high-order matter contributions by considering an interaction term analogous to those in gravitational and spontaneous baryogenesis, constructed using $T^2$. The cutoff energy scale of the new interaction term is presented and its implications to Big Bang Nucleosynthesis (BBN) are discussed. The properties and implications of this term are analyzed within the frameworks of General Relativity and $f(R,T^2)$ gravity. Furthermore, a connection to BBN is established, providing an observational constraint on the functional form of $f(R,T^2)$. By introducing $T^2$ into the gravitational action, we propose that these modifications could significantly influence the early Universe's dynamics, thereby altering the conditions necessary for baryogenesis to occur.