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All current observations suggest that our universe contains an excess of matter over antimatter. The Planck result [1] showed that the left baryon-to-photon ratio is
$ n_B/n_{\gamma} = (6.12\pm 0.04)\times 10^{-10} $ [2]. For theoretical discussions, it is more convenient to use the baryon-to-entropy ratio$ n_B/s $ to quantify this asymmetry, which is approximately$ n_B/s\simeq 8.7\times 10^{-11} $ as calculated from the observational result, as$ s\simeq 7.04 n_{\gamma} $ at present. The origin of this baryon number asymmetry remains unexplained in cosmology. Conventionally, it was argued that this asymmetry was generated dynamically from an initial symmetric baryon phase at the following conditions [3]: (1) baryon number non-conserving interactions, (2)CandCPviolations, (3) a departure from thermal equilibrium.However, if the CPT symmetry is violated, the baryon number asymmetry could be generated in thermal equilibrium [4]. For example, in Refs. [5-7], an effective interaction,
$ {\cal{L}}_{in} = \frac{c}{M_{\ast}}\partial_{\mu}\phi J^{\mu}_B\; , $
(1) between the dynamic dark energy (quintessence) and baryons was introduced, which considers a dimensionless coupling constantcand a cut-off mass scale
$ M_{\ast} $ . As the universe expands, the background evolution of the scalar fieldϕbreaks the Lorentz and CPT symmetries spontaneously, providing an effective chemical potential for baryons and the opposite for antibaryons:$\begin{aligned}[b]& \frac{c}{M_{\ast}}\partial_{\mu}\phi J^{\mu}_B \rightarrow \frac{c}{M_{\ast}}\dot\phi \,n_B = \frac{c}{M_{\ast}}\dot\phi (n_b-n_{\bar{b}})\; ,\\& \mu_b = \frac{c}{M_{\ast}}\dot\phi = -\mu_{\bar{b}}\; . \end{aligned} $
(2) This creates a difference between the distribution functions of baryons and antibaryons in thermal equilibrium, producing an excess of baryons over antibaryons [8]:
$ n_B = \frac{g_b T^3}{6}\left[\frac{\mu_b}{T}+\mathcal{O}\left(\frac{\mu_b}{T}\right)^3\right]\simeq c\frac{\dot\phi T^2}{3M_{\ast}}\; , $
(3)
Gravitational leptogenesis in teleparallel and symmetric teleparallel gravities
- Received Date:2021-09-30
- Available Online:2022-02-15
Abstract:In this study, we investigate the possibilities of generating baryon number asymmetry under thermal equilibrium within the frameworks of teleparallel and symmetric teleparallel gravities. Through the derivative couplings of the torsion scalar and the non-metricity scalar to baryons, baryon number asymmetry is produced in the radiation dominated epoch. For gravitational baryogenesis mechanisms in these two frameworks, the produced baryon-to-entropy ratio is too small to be consistent with observations. However, the gravitational leptogenesis models within both frameworks have the potential to explain the observed baryon-antibaryon asymmetry.
