Slaying Axion-Like Particles via Gravitational Waves and Primordial Black Holes from Supercooled Phase Transition

TL;DR

This work analyzes a radiatively broken global $U(1)$ in an axion-like particle (ALP) model that undergoes a strongly supercooled first-order phase transition, generating a stochastic gravitational wave background and potentially forming primordial black holes (PBHs). The PBH mass scales as $M_{ m PBH}\propto f_a^{-2}$, with the PBH abundance controlled by the nucleation rate parameter $\beta/H_n$ and percolation dynamics, yielding viable DM scenarios with $f_{ m PBH}\approx 1$ in a window $\beta/H_n\sim5-7$, all constrained by BBN, CMB, and microlensing bounds. The GW spectrum from the gauged ALP PT is computed via hybrid simulations, with the amplitude and peak location set by the reheating temperature $T_{ m RH}$ and $\beta/H$, making the signal accessible to LISA, ET, CE, and PTA experiments including NANOGrav; the model can also fit the NANOGrav PTA signal for $f_a\sim(10\text{ GeV}-1\text{ TeV})$ and appropriate gauge coupling. Altogether, the work establishes a direct mapping between ALP properties and PBH/GW observables, providing a robust three-pronged approach to probing ALPs and their cosmological role beyond conventional laboratory searches.

Abstract

We study the formation of primordial black holes (PBHs) from density fluctuations due to supercooled phase transitions (PTs) triggered in an axion-like particle (ALP) model. We find that the mass of the PBHs is inversely correlated with the ALP decay constant $f_a$. For instance, for $f_a$ varying from ${\cal O}$(100 MeV) to ${\cal O}$($10^{12}$ GeV), the PBH mass varies between $(10^{3} - 10^{-24}) M_{\odot}$. We then identify the ALP parameter space where the PBH can account for the entire (or partial) dark matter fraction of the Universe, in a single (multi-component) dark matter scenario, with the ALP being the other dark matter candidate. The PBH parameter space ruled out by current cosmological and microlensing observations can thus be directly mapped onto the ALP parameter space, thus providing new bounds on ALPs, complementary to the laboratory and astrophysical ALP constraints. Similarly, depending on the ALP couplings to other Standard Model particles, the ALP constraints on $f_a$ can be translated into a lower bound on the PBH mass scale. Moreover, the supercooled PT leads to a potentially observable stochastic gravitational wave (GW) signal at future GW observatories, such as aLIGO, LISA and ET, that acts as another complementary probe of the ALPs, as well as of the PBH dark matter. Finally, we show that the recent NANOGrav signal of stochastic GW in the nHz frequency range can be explained in our model with $f_a\simeq (10~{\rm GeV}-1~{\rm TeV})$.

Figures (13)

• Figure 1: Contours showing the nucleation temperature $T_n$ (in units of $f_a$) and the $\beta/H$ parameter in the plane of the model parameters $f_a$ and $g$. In the gray region nucleation never occurs.
• Figure 2: The fraction of DM in the form of PBH, $f_{\rm PBH}$, as functions of the two parameters of the model, $g$ (left panel) and $f_a$ (right panel), with constant contours of the other parameter shown. The gray region corresponds to PBH overclosure.
• Figure 3: PBH and GW predictions in our scale-invariant $SU(2)$ realization of the ALP model. Some contours of $f_{\rm PBH}$ (purple), $\alpha$ and $\beta/H$ are shown. The gray and red shaded regions are disfavored. The thick red line shows the allowed region where PBHs can explain 100% DM relic. The blue shaded regions are the $2\sigma$ preferred regions to explain the NANOGrav signal. Other solid/dashed lines correspond to the sensitivities of the future GW detectors. See text for further details.
• Figure 4: Same as Fig. \ref{['fig:fa_g']} but zoomed in around the $f_{\rm PBH}=1$ line. Also shown are some relevant $M_{\rm PBH}$ contours (in units of $M_\odot$).
• Figure 5: The GW spectra predicted in our ALP model are shown by the colored solid lines corresponding to different values of $f_a$, which have a one-to-one correspondence with the PBH mass (for a fixed $f_{\rm PBH}=1$). Five benchmark points (A to E) are marked here, which will be used later. The areas above the colored dotted lines correspond to the projected sensitivities for several current and future GW observatories. The horizontal lines show current $\Delta N_{\rm eff}$ constraints from BBN and Planck data (shaded regions) and future reaches by CMB-S4, CMB-Bharat and CMB-HD. The red shaded region on top right is the current exclusion from LIGO-VIRGO data. The blue violins on the top left are the recent NANOGrav data points for the SGWB detection. The shaded region on the bottom half of the plane is the expected astrophysical foreground. See text for details.