Gravitational baryogenesis in $f(T,L_m)$ gravity

TL;DR

This paper investigates gravitational baryogenesis within f(T,L_m) gravity, focusing on three torsion–matter coupling models and three CPT-violating interaction forms. By deriving the modified Friedmann dynamics and computing the baryon-to-entropy ratio at the freeze-out temperature T_D, it finds that couplings involving both torsion and L_m, particularly ∂_μ(-T - L_m/L_0), can yield the observed asymmetry for decoupling temperatures around TD ∼ 10^{12}–10^{14} GeV while keeping MG contributions small. In contrast, a pure ∂_μ(-T) coupling struggles to produce sufficient asymmetry within the same TD range, and fully general ∂_μ(f(T,L_m)) couplings typically require large coupling magnitudes that conflict with the MG constraint. The results demonstrate that nonminimal torsion–matter couplings in f(T,L_m) gravity provide a viable framework for early-Universe baryogenesis and remain compatible with late-time ΛCDM cosmology, suggesting a unified picture for early- and late-time dynamics within teleparallel gravity. These findings highlight the potential of f(T,L_m) theories to realize CPT-violating baryogenesis while preserving standard cosmological evolution at late times.

Abstract

The observed matter-antimatter asymmetry of the Universe remains a fundamental challenge in modern physics. In this work, we explore gravitational baryogenesis within the framework of $f(T,L_m)$ gravity, where the gravitational Lagrangian depends on both the torsion scalar $T$ and the matter Lagrangian $L_m$. We consider three representative models and examine their ability to generate the observed baryon-to-entropy ratio. Our analysis shows that couplings involving both torsion and the matter Lagrangian, $\partial_μ(-T-\frac{L_m}{L_0})$, can successfully account for the baryon asymmetry for decoupling temperatures in the range $10^{12}$-$10^{14}\,\text{GeV}$, while remaining consistent with small deviations from General Relativity. These results highlight the capacity of $f(T,L_m)$ gravity to provide novel mechanisms for baryogenesis, demonstrating that the interplay between torsion and matter-sector contributions can naturally generate the observed asymmetry. The framework also remains compatible with late-time cosmological evolution, offering a unified setting for early- and late-time dynamics.

Figures (12)

• Figure 1: Plot of the baryon to entropy ratio for model $f=BTL_m$ for varying B, $\mathbf{T}_D=10^{16}\ GeV$, $M_*=2.4\times 10^{17}\ \text{GeV}$, $\epsilon=1$, $n=\frac{1}{2}$ and $w=\frac{1}{3}$.
• Figure 2: Plot of the baryon to entropy ratio for model $f=B(1-e^{-p\sqrt{|T|}})L_m$ for varying B, $\mathbf{T}_D=10^{16}\ \text{GeV}$, $M_*=5\times 10^{17}\ \text{GeV}$, $p=-10^{-16}\, \mathrm{GeV}^{-1}$ , $\epsilon=1$, $n=\frac{1}{2}$ and $w=\frac{1}{3}$.
• Figure 3: Plot of the baryon to entropy ratio for model $f=B(1-e^{-pT})L_m$ for varying B, $\mathbf{T}_D=10^{16}\ \text{GeV}$, $M_*=1\times 10^{17}\ GeV$, $p=10^{-30}\, \mathrm{GeV}^{-2}$, $\epsilon=1$$n=\frac{1}{2}$ and $w=\frac{1}{3}$.
• Figure 4: Plot of the baryon to entropy ratio for model $f=BTL_m$ for varying B, $\mathbf{T}_D=10^{9}\ \text{GeV}$, $M_*=1\times 10^{13}\ \text{GeV}$, $\epsilon=-1$, $n=\frac{1}{2}$ and $w=\frac{1}{3}$.
• Figure 5: Plot of the baryon to entropy ratio for model $f=B(1-e^{-p\sqrt{|T|}}) L_m$ for varying B, $\mathbf{T}_D=10^{8}\ \text{GeV}$, $M_*=1\times 10^{10}\ \text{GeV}$, $p=-10^{-11}\ \text{GeV}^{-1}$, $\epsilon=-1$ , $n=\frac{1}{2}$ and $w=\frac{1}{3}$