Baryogenesis constraints and parameter bounds in $f(T,T_G)$ modified gravity

We investigate the generation of the observed baryon asymmetry of the Universe within the framework of $f(T,T_G)$ gravity, where $T$ is the torsion scalar and $T_G$ denotes its teleparallel Gauss–Bonnet counterpart. Two illustrative models, $f(T,T_G)=\alpha T+\beta \sqrt{T_G}$ and $f(T,T_G)=-T+\delta T_G\ln (T_G)$, are examined in a power-law background $a(t)=a_0{t}^m$. For both models, we derive analytic expressions for the baryon-to-entropy ratio ${\eta }_B\mathrm{/}s$ using the standard and generalized baryogenesis formalisms, adopting high-energy decoupling conditions with $g_b=1$, $g_s=106$, $T_D=2\times {10}^{16}\mathrm{G}\mathrm{e}\mathrm{V}$, and $M_{\star }=2\times {10}^{12}\mathrm{G}\mathrm{e}\mathrm{V}$. Consistency of the cosmological dynamics requires $m>1$, and the observed value ${\eta }_B\mathrm{/}s\simeq 9.42\times {10}^{-11}$ is obtained for constrained intervals of the parameters $\alpha$, $\beta$, $\delta$, and $m$. Numerical results confirm that both models reproduce the measured baryon asymmetry without invoking extra fields or exotic matter sources. These findings indicate that teleparallel gravity with a Gauss–Bonnet torsion term provides a natural and viable mechanism for baryogenesis, offering a compelling alternative to curvature-based descriptions of the early Universe.