Vector-field spontaneous baryogenesis with Lorentz invariance violation

TL;DR

This work extends spontaneous baryogenesis by introducing a complex vector field that spontaneously breaks U(1)_B and, simultaneously, Lorentz invariance via a spacelike Bumblebee vacuum. The pseudo-Nambu-Goldstone mode θ, arising from the U(1)_B breaking, acts as the inflaton and couples through a vector-current interaction that violates CP and baryon number, driving baryogenesis during inflation and reheating. Flavor oscillations induced by the LV background modify the baryon production, yielding a nonzero asymmetry even for massless fermions and allowing comparatively larger coupling constants than in scalar-based models. Restoring Lorentz symmetry at late times is discussed within Bumblebee-type scenarios, and the model can reproduce the observed baryon-to-entropy ratio for moderate couplings, offering a novel LIV-based mechanism with potential connections to high-energy cosmology and quantum gravity effects.

Abstract

We extend spontaneous baryogenesis by considering the spontaneous breaking of $U(1)_B$ through a complex vector field. This field interacts with baryons and leptons via a vector-current coupling and, by construction, acquires a nonzero vacuum expectation value. Accordingly, the theory also exhibits a spontaneous violation of Lorentz invariance, effectively realizing a Bumblebee model. In this picture, the pseudo-Nambu-Goldstone boson arising from spontaneous breaking of the $U(1)_B$ global symmetry is the global phase of the Bumblebee vector and, in the broken phase, it results minimally coupled with the baryonic current, guaranteeing the violation of the baryon number. Consequently, we assume that the pseudo-Nambu-Goldstone, arising from spontaneous breaking of $U(1)_B$, plays the role of the inflaton, leading to baryogenesis across the entire inflationary stage, up to when the inflaton decays into baryon-antilepton and antibaryon-lepton pairs through a CP-violating interaction that also violates the Lorentz symmetry. Afterwards, we address the issue of flavor oscillations among baryon and lepton fields, including the oscillation probability in the calculation of the baryon asymmetry. Remarkably, our framework predicts a non-null mixing factor even for massless fermions. This mixing acts on the spatial momenta rather than on the masses of the produced fermions, allowing larger values of the coupling constant even guaranteeing the production of light fermions. The net baryon asymmetry results accordingly modified, and may also reproduce the experimental data for allowed values of the coupling constant.

Figures (3)

• Figure 1: Continuous line: function $\mathcal{P}(c)$ numerically computed with respect to the normalized momentum $c$, obtained for $g=10^{-3}$. Dotted line: limit value of the $\mathcal{P}(c)$ for low momenta, $\lim_{c\to 0}\mathcal{P}(c)=1$. Dashed line: limit value of the $\mathcal{P}(c)$ for high momenta, $\lim_{c\to+\infty}\mathcal{P}(c)=[\text{Si}(4/b)]/[4/b]$.
• Figure 2: Continuous line: function $\mathcal{I}(g)$ numerically computed accounting for the $Q-L$ oscillations. Dashed line: theoretical curve $\mathcal{I}_0(g)=12\pi^2/g^2$, obtained for $\mathcal{P}(c)=1$. Dotted line: best fit of $\mathcal{I}(g)$ through the model of the constant function, that provides the value $\eta=1.105$.
• Figure 3: Comparison between the baryon-to-entropy ratio obtained within SSB, by Eq. (\ref{['eq141']}), and VFSB, by Eq. (\ref{['eq140']}). In particular, the first one is obtained in the limit $\Delta m\ll gf$, considering light fermions but not totally massless, whereas the second in the purely massless fermions limit. The dark (light) colored region is the region of parameter space where VFSB predicts a baryon asymmetry higher (lower) than SSB.