Observational constraining on baryon to entropy ratios in modified theories of gravity

Baryogenesis, the generation of the cosmic matter-antimatter asymmetry, remains one of the profound questions in theoretical physics. This research explores the mechanisms of baryogenesis and extends the investigation to its more generalized theoretical frameworks within the context of squared energy–momentum theories, specifically $f(R,T^2)$, $f(G,T^2)$ and $f(Q,T^2)$. These theories extend conventional general relativity by incorporating novel couplings between the trace of the energy–momentum squared tensor, $T^2\equiv T_{\mu \nu }{T}^{\mu \nu }$, and fundamental geometric scalars: the Ricci scalar $R$, the Gauss–Bonnet invariant $G$, and the non-metricity scalar $Q$. We consider two generic models within each theory to explore their implications on the dynamical evolution of the early universe and their potential role in generating the observed baryon asymmetry. By analyzing the interplay between gravity and particle physics in the high-energy regime, we derive conditions under which baryogenesis can occur in each theory. Furthermore, by integrating the power law scale factor into our models, we examine its impact on the baryogenesis mechanism and resulting matter-antimatter asymmetry. Through detailed numerical simulations and analytical calculations, we assess the viability of each model in generating the observed baryon asymmetry, contributing to a deeper understanding of the connection between gravitational theories and fundamental processes in cosmology. These findings pave the way for future experimental tests and observational constraints on these theories.