How light can ALP dark matter be?

TL;DR

This work evaluates axion-like particles as the sole dark matter candidate, deriving lower bounds on the ALP mass by merging post- and pre-inflation scenarios. It revisits isocurvature constraints in the post-inflationary case by incorporating axion radiation from a cosmic-string network, finding substantially weaker limits than earlier works, and adds a complementary bound from non-detection of CMB tensor modes that depends on the reheating efficiency. In the pre-inflationary case, the analysis emphasizes a scale-invariant isocurvature spectrum and strong BH superradiance constraints, while comparing the two histories to map allowed regions in the $m_a$–$E_I$ plane. The results collectively disfavor very light fuzzy-mass ALP DM and highlight the critical role of the inflationary energy scale and the detailed string-emission spectrum in shaping viable parameter space.

Abstract

We assume axion-like particles (ALPs) to provide the full dark matter abundance and derive various lower bounds on the ALP mass. We contrast the post- and pre-inflationary symmetry breaking cases and present allowed regions in the plane of ALP mass and energy scale of inflation. For the post-inflationary case, we revisit bounds from isocurvature perturbations taking into account that, as suggested by simulations, axion radiation by cosmic strings during the scaling regime provides the dominant production mechanism of dark matter, obtaining significantly weaker limits than previously. Combining isocurvature, with constraints from black hole superradiance and free streaming, we find that the bound $m_a \gtrsim 10^{-17}$ eV applies for most cases considered here. It can be potentially relaxed to $\sim 6\times 10^{-19}$ eV only in the post-inflationary case with a strongly temperature-dependent axion mass, subject to uncertainties on the axion emission spectrum. Significantly stronger bounds are obtained in the post-inflationary scenario from the non-observation of CMB tensor modes, which can be as strong as $m_a > 5\times 10^{-7}$ eV for small reheating efficiencies, $ε\lesssim 5\times 10^{-4}$.

Figures (12)

• Figure 1: Axion decay constant $f_a$ vs. axion mass $m_a$ in the post-inflationary scenario, for different $\alpha,\,\beta$ and for $q > 1$, assuming that axions radiated by cosmic strings during the scaling regime constitute all of dark matter. Shaded regions above the curves overproduce dark matter. The band width reflects $\beta$ = 0.1--10, with the lower (upper) boundary corresponding to 0.1 (10). The IR momentum cutoff is $k_{\rm min} = x_0\sqrt{\xi_*H_*H}$ with $x_0 = 10$. Vertical solid (dashed) lines indicate the lower bound on $m_a$ from isocurvature constraints using UFDs (21 cm), see \ref{['sec:iso-post']}. The blue and green dashed lines overlap. Horizontal lines indicate the upper bound on $f_a$ from CMB tensor modes, depending on the reheating efficiency $\epsilon$ with $\epsilon_{\rm crit} = 5.4\times 10^{-4}$, see \ref{['sec:tensor-modes']}. Also shown are the lower bound on $m_a$ from free streaming (FS), \ref{['eq:ly-a_ma_bound_post']}Liu:2024pjg, regions excluded by BH superradiance Unal:2020jiyWitte:2024drg, and the QCD axion (yellow line) with the star marking where the QCD-like $m_a(T)$ gives the correct dark matter abundance.
• Figure 2: Same as \ref{['fig:strings_abundance_q3']} but for a scale-free axion emission spectrum ($q=1$).
• Figure 3: Isocurvature power spectrum according to \ref{['eq:P_iso']} for $m_a = 10^{-11}$ eV and model parameters as indicated in the figure. $f_a \simeq 10^{13}$ GeV has been determined from requiring full dark matter abundance. The dotted line indicates the corresponding value of the IR cutoff $k_{\rm min,\ast}$. The dashed line corresponds to the analytic expression for small $k$ from \ref{['eq:Delta']}.
• Figure 4: Comoving size of the IR spectrum cutoff as a function of $m_a$, with $f_a$ determined by requiring full dark matter abundance. Left:$k_{\mathrm{min},*}$ for $q=1$ and various choices of $\alpha$ and $\beta$. The parameter $x_0$ is fixed to 10; modifying its value leads to an approximately linear rescaling of $k_{\mathrm{min},*}$. Right: Comparison of $k_{\mathrm{min},*}$ to the peak momentum $k_{\rm peak}= m_\ell$ after the nonlinear transition at $T_\ell$ and $k_{\rm peak}= k_{\rm vir}$ after the nonlinear transition due to self-interactions at $T_c$. For comparison, we also show the comoving momentum corresponding to $m_a$ at $T_c$.
• Figure 5: Predicted isocurvature fraction $f_{\rm iso}$ vs. axion mass $m_a$, assuming 100% dark matter abundance for different parameter choices $q,\,\alpha\text{ and } \beta$, compared to the upper bounds from Lyman-$\alpha$ and UFD (black solid), as well as 21 cm sensitivity (black dashed), see \ref{['tab:fiso-limits']}. The grey-shaded region indicates the lower bound on $m_a$ from free streaming, \ref{['eq:ly-a_ma_bound_post']}Liu:2024pjg. For low $m_a$, the UFD constraint weakens, depending on $q,\,\alpha,\,\beta$, but in all cases it intersects the corresponding prediction roughly at the same value of $f_{\rm iso} = 6\times 10^{-4}$.