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 $\eta_{B}/s$ using the standard and generalized baryogenesis formalisms, adopting high-energy decoupling conditions with $g_{b}=1$, $g_{s}=106$, $T_{D}=2\times10^{16}\,\mathrm{GeV}$, and $M_{\star}=2\times10^{12}\,\mathrm{GeV}$. Consistency of the cosmological dynamics requires $m>1$, and the observed value $\eta_{B}/s \simeq 9.42\times10^{-11}$ 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.