Axion Dark Matter Archaeology with Primordial Gravitational Waves

TL;DR

This work shows that post-inflationary Peccei–Quinn breaking axion models with heavy-quark domination can yield viable axion dark matter masses as low as $m_a\sim10^{-8}$ eV, provided heavy quarks decay via dimension-$d\ge6$ operators. HQD alters the axion misalignment via nonstandard cosmology, diluting the axion abundance and complicating the distinction between pre- and post-inflationary PQ breaking unless complementary probes are used. The authors propose blue-tilted inflationary gravitational waves as a key diagnostic: the HQD epoch imprints distinctive features on the stochastic GW background, allowing interferometers (ET, BBO, LISA, etc.) to constrain $m_Q$ and $\Lambda$, thereby complementing haloscope searches that pin down $f_a$. By combining GW observations with axion haloscopes, one can reconstruct the relevant high-scale physics, including the anomaly structure $E/N$ and the axion-photon coupling $g_{a\gamma}$, while also testing the inflationary dynamics through $n_T$ and $r$. The results indicate substantial regions of parameter space where future GW detectors and haloscopes can jointly probe HQD scenarios, offering a pathway to reveal the early-universe conditions that shaped axion dark matter.

Abstract

We investigate the complementary information to be gained from inflationary gravitational wave (IGW) signals and searches for QCD axion dark matter. We focus on post-inflationary Peccei-Quinn (PQ) breaking axion models that are cosmologically safe. Recent work has shown that a greater number of such models exist. This is because the heavy quarks required for the colour anomaly can provoke a period of heavy quark domination (HQD), which, through decay, dilutes the axion abundance. In this work we show for the first time that the axion dark matter mass can be as low as $m_a\sim10^{-8}\,{\rm eV}$ for models where the heavy quarks decay via dimension 6 terms. This is achieved by allowing the mass of the heavy quarks to differ from the axion decay constant, $m_Q\neq f_a$. Consequently, the observables that would distinguish between pre- and post-inflationary PQ breaking, $m_a$ and the additional relativistic degrees of freedom $ΔN_{\rm eff}$, now become indiscernible. To solve this, we propose using blue-tilted IGWs to probe HQD. In scenarios where such a blue tilt is present, the enhanced GW signal allows future interferometers to place non-trivial constraints on the parameters $m_Q$ and $f_a$, thereby complementing haloscope searches. While some degeneracies with other parameters such as $m_Q$ remain, detectors such as BBO and ET will be able to optimistically probe $f_a\gtrsim 10^{14}\,{\rm GeV}$.

Figures (12)

• Figure 1: The range of axion mass $m_a$ which can reproduce the correct relic abundance allowing for any $m_Q\lesssim f_a$ and $\Lambda<m_{\rm Pl}$. This is for $d=6$ but we find the result for $d=7$ decays to be very similar. The axion limits and QCD axion band was plotted using Ref. AxionLimits.
• Figure 2: The current constraints on the $m_Q$ and $\Lambda$ parameter space from ADMX and CAPP experiments. The left panel is for $d=6$ decays and the right panel is for $d=7$ decays. The value of $f_a$ is not a priori set, instead we determine the required value such that $\Omega_a=\Omega_{\rm cdm}$. The hatched region is where $Q$ decay occurs too late and will be constrained by BBN, we have bounded it by the dotted and solid black lines which correspond to the more approximate Eq. (\ref{['eq:Tdec']}) and precise numerical evaluation via Eqs. (\ref{['eq:FBEqs_FEq']}) respectively.
• Figure 3: Illustration of GW spectrum for different values of $m_Q$, $d$ and $T_{\rm RH}$, compared with the standard scenario (without HQD) via thin grey solid line. In each of the GW spectrum (dashed, dot-dashed, dotted), variation with respect to parameters are quoted. Grey hatched regions are the excluded regions by the existing constraints (Planck-18+BAO, BBN and LIGO). Left panel is for $n_T = 0$, whereas Right panel is for $n_T=0.5$. Here $m_Q$ and $T_{\rm RH}$ are in GeV. For both of the plots $r=0.036$ is fixed which corresponds to the Hubble scale of inflation $H_{\rm inf}\sim10^{13}$ GeV.
• Figure 4: SNR in the $n_T-r$ plane across several GW detectors. Left panel corresponds to the standard scenario (without HQD) whereas right panel presents the HQD scenario for the same set of benchmark parameters ($m_Q=10^{14}$ GeV, $d=6$ and $\Lambda=m_{\rm Pl}$) as in Fig. \ref{['fig:GW_spectrum']}. The purple star and circle in the right panel mark the benchmark point in the $n_T-r$ plane, which are also utilized in Fig. \ref{['fig:GW_spectrum']}. Both panels assume $T_{\rm RH}=10^{16}$ GeV. Coloured lines correspond to $\rm SNR=10$ contour for the respective detector, with the region to the right $\rm SNR>10$. Hatched region presents the excluded region by Planck-18+BAO due to overproduction GWs.
• Figure 5: Illustration of SNR in the $m_Q-\Lambda$ plane for LISA across different dimensions. Black solid line represents ${\rm SNR}=10$, with the region below this line corresponding to ${\rm SNR} > 10$, as indicated by the colour scale. The gray-shaded region denotes the parameter space excluded by BBN constraints due to the overproduction of gravitational waves. Both the dimensions are for $n_T=0.5$ and $r=0.036$.