Cosmological properties of a gauged axion

We analyze the most salient cosmological features of axions in extensions of the standard model with a gauged anomalous extra $U(1)$ symmetry. The model is built by imposing the constraint of gauge invariance in the anomalous effective action, which is extended with Wess-Zumino counterterms. These generate axionlike interactions of the axions to the gauge fields and a gauged shift symmetry. The scalar sector is assumed to acquire a nonperturbative potential after inflation, at the electroweak phase transition, which induces a mixing of the Stückelberg field of the model with the scalars of the electroweak sector, and at the QCD phase transition. We discuss the possible mechanisms of sequential misalignments which could affect the axions of these models, and generated, in this case, at both transitions. We compute the contribution of these particles to dark matter, quantifying their relic densities as a function of the Stückelberg mass. We also show that models with a single anomalous $U(1)$ in general do not account for the dark energy, due to the presence of mixed $U(1)-SU(3)$ anomalies.

Figure 1

Anomalous contributions to the Lagrangian and WZ counterterms.

Figure 2

Contributions to the $\chi \to \gamma \gamma$ decay.

Figure 3

Total decay rate of the axi-Higgs for several mass values. Here, for the PQ axion, we have chosen $f_a={10}^{10}\mathrm{GeV}$.

Figure 4

Relic density of the axi-Higgs as a function of $\tan \beta$.

Figure 5

Relic density of the axi-Higgs as a function of $M$. The grey bar represents the measured value of ${\Omega }_{\mathrm{DM}}{h}^2=0.1123\pm 0.0035$.