Baryogenesis constraints and parameter bounds in $f(T,T_{G})$ modified gravity

TL;DR

The work investigates gravitational baryogenesis within the teleparallel framework extended by a Gauss–Bonnet torsion term, $f(T,T_G)$. Using a power-law cosmology $a(t)=a_0 t^m$, the authors derive analytic expressions for the baryon-to-entropy ratio $η_{B}/s$ under both standard and generalized baryogenesis formalisms for two explicit models: $f(T,T_G)=\alpha T+\beta\sqrt{T_G}$ and $f(T,T_G)=-T+\delta T_G\ln(T_G)$. They find that the observed value $η_{B}/s \simeq 9.42\times 10^{-11}$ can be achieved within constrained parameter ranges (e.g., $m>1$ with specific $(α,β)$ for Model 1 and $δ$ bounds for Model 2) without invoking additional fields. The results demonstrate that torsion-based modifications of gravity can naturally account for the baryon asymmetry, offering a curvature-free alternative to curvature-based baryogenesis while motivating further study of perturbations and reheating in these theories.

Abstract

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, $f(T,T_{G})=αT+β\sqrt{T_{G}}$ and $f(T,T_{G})=-T+δ\, T_{G}\ln(T_{G})$, 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 $η_{B}/s$ 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 $η_{B}/s \simeq 9.42\times10^{-11}$ is obtained for constrained intervals of the parameters $α$, $β$, $δ$, 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.

Figures (4)

• Figure 1: Variation of the baryon-to-entropy ratio $\frac{\eta_{B}}{s}$ with respect to the power-law index $m$ for the Model 1$f(T,T_{G})=\alpha T+\beta \sqrt{T_{G}}$. The curves correspond to three different values of $\beta$, while the other model parameters are fixed at $g_{b}=1$, $g_{s}=106$, $T_{D}=2\times 10^{16}\,\text{GeV}$ and $M_{\star}=2\times 10^{12}\,\text{GeV}$. The plot shows that all parameter choices successfully reproduce the observed constraint $\frac{\eta_{B}}{s}\simeq 9.42\times 10^{-11}$.
• Figure 2: Plot of the baryon-to-entropy ratio $\frac{\eta_{B}}{s}$ versus the power–law parameter $m$ for the generalized baryogenesis scenario of Model 1$f(T,T_{G})=\alpha T+\beta \sqrt{T_{G}}$. All curves satisfy the observational bound $\frac{\eta_{B}}{s}\simeq 9.42\times 10^{-11}$.
• Figure 3: Plot of the baryon-to-entropy ratio $\frac{\eta_{B}}{s}$ versus the power–law parameter $m$ for the Model 2$f(T,T_{G})=-T+\delta\; T_{G}\;\log(T_{G})$. All trajectories intersect the observational bound $\frac{\eta_{B}}{s}\simeq 9.42\times 10^{-11}$, demonstrating the viability of the model across the chosen parameter space.
• Figure 4: Plot of the baryon-to-entropy ratio $\frac{\eta_{B}}{s}$ as a function of the model parameter $m$ of the Model 2$f(T,T_{G})=-T+\delta\; T_{G}\;\log(T_{G})$ for three different values of $\delta$. The plot shows that observational baryogenesis criteria can be satisfied within well-defined ranges of $m$ for each choice of $\delta$.