Nonthermal axion dark radiation and constraints

The Peccei-Quinn mechanism presents a neat solution to the strong $CP$ problem. As a by-product, it provides an ideal dark matter candidate, “the axion”, albeit with a tiny mass. Axions therefore can act as dark radiation if excited with large momenta after the end of inflation. Nevertheless, the recent measurement of relativistic degrees of freedom from cosmic microwave background radiation strictly constrains the abundance of such extra relativistic species. We show that ultrarelativistic axions can be abundantly produced if the Peccei-Quinn field was initially displaced from the minimum of the potential. This in lieu places an interesting constraint on the axion dark matter window with large decay constant which is expected to be probed by future experiments. Moreover, an upper bound on the reheating temperature can be placed, which further constrains the thermal history of our Universe.

Figure 1

Observational constraints on the reheating temperature $T_{\mathrm{rh}}$ and the axion decay constant $f_a$. In the region shaded in dark orange, $\sigma$ comes to dominate the energy density of the Universe before it decays and hence is ruled out. The adjacent hatched region shaded in lighter orange is ruled out by the CMB bound on $N_{\mathrm{eff}}$. The blue region is ruled out by laboratory experiments and the observation of supernova SN1987A and globular cluster stars. In the yellow region, the PQ symmetry gets thermally restored. The vertical dotted black lines indicate the CDM upper bound on $f_a$ whereas the vertical solid red lines refer to the isocurvature upper bound on $f_a$ for different values of misalignment angle. For ${\theta }_i=1$, the entire parameter space is ruled out by the CMB bound on the isocurvature perturbations. Note that the isocurvature bound need not apply if $\varphi$ were a moduli field, the issue is rather model dependent.

Figure 2

Same as Fig. 1 but for $m_{\varphi }=10^{10}\mathrm{GeV}$ and $\lambda ={10}^{-17}$.