Gravitational Baryogenesis in Energy-Momentum Squared Gravity

We demonstrate that the matter sector itself can drive baryogenesis in energy-momentum squared gravity, f(R,T2) with T2≡TμνTμν. High-density matter corrections provide new time-dependent sources for the baryon asymmetry through derivative couplings to T2 and to the full combination f(R,T2). Notably, the decoupling temperature is not treated as a free parameter; instead, it is fixed by the freeze-out of the Weinberg B−L-violating operator, directly linking the asymmetry to the light-neutrino mass scale and to the modified expansion history. Analyzing representative powers n=1/4, n=1/2, n=5/8, and n=1, we find that entropy evolution sharply distinguishes the models. The n=1/4 branch cannot serve as a self-contained radiation-era model, the n=1/2 branch is entropy-safe but too weak to reproduce the observed asymmetry, and the n=1 branch survives only after entropy dilution. Remarkably, the n=5/8 branch provides the cleanest viable realization, generating the observed baryon-to-entropy ratio with controlled effective-field-theory hierarchies.