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Description
This work investigates the generation of the observed matter--antimatter asymmetry of the Universe within the framework of $f(T,T_G)$ gravity, where $T$ is the torsion scalar and $T_G$ is its teleparallel Gauss--Bonnet counterpart. In this study, we consider two illustrative modified gravity models, $f(T,T_G)=f(T,T_{G})=\alpha T+\beta\sqrt{T_{G}}$ and $f(T,T_{G})=-T+\delta\; T_{G}\;\log(T_{G})$, within a cosmological background evolving according to a power-law scale factor, $a(t)=a_0 t^m$. Analytic expressions for the baryon-to-entropy ratio $\frac{\eta_B}{s}$ are obtained directly from the modified field equations for each of the two baryogenesis formulations, standard and generalized. The analysis employs high-energy decoupling conditions with $g_{b}=1$, $g_{s}=106$, $T_{D}=2\times 10^{16}\,\text{GeV}$ and $M_{\star}=2\times 10^{12}\,\text{GeV}$. In both frameworks, imposing the condition $m>1$ maintains the reality and consistency of the cosmological dynamics, and the observational value $\frac{\eta_B}{s}\simeq 9.42 \times 10^{-11}$ can be reproduced for specific, well-constrained intervals of the parameters $\alpha$, $\beta$, $\delta$ and $m$. Numerical exploration supported by graphical and tabulated results shows that both models successfully reproduce the observed baryon asymmetry without introducing extra fields or exotic matter components. These results demonstrate that teleparallel gravity modified by the inclusion of the Gauss–Bonnet torsion term can naturally produce the required baryon asymmetry, making it a strong contender to replace conventional curvature-based models of the early Universe.