Gravitational Baryogenesis in Energy-Momentum Squared~Gravity
We demonstrate that the matter sector itself can drive baryogenesis in energy-momentum squared gravity, $f(R,\mathcal T^2)$ with $\mathcal T^2\equiv T_{μν}T^{μν}$. High-density matter corrections provide new time-dependent sources for the baryon asymmetry through derivative couplings to $\mathcal T^2$ and to the full combination $f(R,\mathcal T^2)$. 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.