Nucleosynthesis and CMB bounds on photophilic ALPs: a fresh look

TL;DR

The paper addresses the cosmological constraints on photophilic ALPs with $\tau_a\lesssim 10^{4}\,\mathrm{s}$ and $m_a\lesssim 10\,\mathrm{GeV}$, highlighting the importance of rare hadronic decays in shaping the bounds across a wide range of reheating temperatures $T_{\rm reh}$. The authors develop a comprehensive, model-independent framework that couples ALP production via Primakoff and $\gamma\gamma$ fusion, hadronic decay channels through the $R(s)$ ratio, and a self-consistent treatment of the early-Universe thermodynamics and the BBN network, including meson-driven $p\leftrightarrow n$ conversions. Their results strengthen and broaden previous bounds, revealing a new hadronic island around $m_a\in[0.5,10]\,\mathrm{GeV}$ for moderate $T_{\rm reh}$ and showing that meson decays can either tighten or redirect the exclusion regions; they also identify parameter regions where ALPs could modestly alleviate tensions in $N_{\rm eff}$ and ${\rm D/H}|_{\rm P}$. The work provides a robust, publicly shareable analysis framework that can be adapted to generic relics decaying to photons and broadened to other couplings, with important implications for cosmology and string-m motivated ALP landscapes.

Abstract

We provide a fresh look at the cosmological constraints on axion-like particles (ALPs) that couple predominantly to photons, focusing on lifetimes $τ_{a} \lesssim 10^{4}\, {\rm s}$ and masses $m_a\lesssim 10\,{\rm GeV}$. We consider Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) bounds and explore how these limits depend upon the unknown reheating temperature of the Universe, $T_{\rm reh}$. Compared with some previous studies, we account for the rare decays of these ALPs into light hadrons and show that this leads to extended constraints for several reheating temperatures. Our limits are cast in a model-independent way, and we identify regions of parameter space where these ALPs could alleviate small tensions in the determinations of $N_{\rm eff}$ and the deuterium abundance.

Figures (11)

• Figure 1: ALP parameter space. Left panel: plane mass-lifetime, showing cosmological constraints in the scenario with a high reheating temperature $T_{\rm reh}\ge 10^{10}\,{\rm GeV}$ (see Fig. \ref{['fig:results-ALPs-reheating-temperature']} for other choices of $T_{\rm reh}$). The blue domain shows the constraints from primordial helium-4 abundance observations ($Y_{\rm P}$), the cyan one -- from the primordial deuterium abundance (${\rm D/H}|_{\rm P}$), while the purple one corresponds to the bounds from $N_{\rm eff}$ measurements. The light-red band corresponds to the range of masses and lifetimes where ALPs cause $N_{\rm eff}\xspace = 2.81\pm 0.12$, preferred by the latest CMB measurements (see Sec. \ref{['sec:methodology']} for details). Right panel: the results in the plane ALP mass-coupling $g_{a\gamma\gamma}$, where we also show cosmological and astrophysical bounds, as well as the sensitivity of the recently approved SHiP experiment SHiP:2025ows, whose projected reach is among the leading probes of long-lived, GeV-mass ALPs deBlas:2025gyz. The results for $\tau_{a}<10^{4}\,{\rm s}\xspace$ are as obtained in this work. The larger lifetimes are excluded by the combination of various bounds emerging on electromagnetically decaying thermal relics Poulin:2016anjKawasaki:2017bqmLanghoff:2022bij.
• Figure 2: The cosmological constraints on ALPs interacting with photons shown for several values of the reheating temperature $T_{\rm reh}\xspace = 5\,{\rm MeV}\xspace, 200\text{ GeV}, 10^{10}\text{ GeV}$. The bounds combine constraints from $N_{\rm eff}$, $Y_{\rm P}$, and $\text{D}/\text{H}|_{\rm P}$. The island for $T_{\rm reh}\xspace = 200\,{\rm GeV}\xspace$ results from the impact of the rare decays of the ALP into hadrons, see text for more details. We refer to Fig. \ref{['fig:comparison-robust']} in appendix where we show limits for $T_{\rm reh}\xspace = 10\,{\rm MeV}\xspace, 1\text{ GeV}, 10^3\text{ GeV}, 10^6\text{ GeV}$.
• Figure 3: The cosmological constraints on a particle $X$ that primarily decays into $\gamma \gamma$ and with abundance $Y_{X} = n_{X}/s$ at $T = 20\,{\rm MeV}\xspace$ (assuming that it is fully decoupled), mass $m_{X}$, and lifetime $\tau_{X}$, in the plane $Y_{X}\cdot m_{X}$ vs $\tau_{X}$. Several values of the mean number of pions per $X$ decay and mass are shown: $m_{X} = 100\,{\rm MeV}\xspace, \text{Br}_{X\to \pi}=0$ (top left), $460\,{\rm MeV}\xspace,6\cdot 10^{-6},$ (top right), $535\,{\rm MeV}\xspace,2\cdot 10^{-5}$ (bottom left), and $4.5\,{\rm GeV}\xspace,10^{-2}$ (bottom right) corresponding to the $\text{Br}_{X\to \pi}$ expected from our calculation in Sec. \ref{['sec:methodology']}. The green domains correspond to the region preferred by the combination of $\text{D}/\text{H}|_{\rm P}$ and $N_{\rm eff}$ measurements, see the discussion around Eq. \ref{['eq:preferred-DH-Neff']}. The plot may be mapped onto the ALP parameter space in scenarios with arbitrary cosmological setups; we indicate this map by showing the iso-contours of the ALP abundance with the mass $m_{a} = m_{X}$ for fixed reheating temperatures $T_{\rm reh}\xspace$.
• Figure 4: Left panel: the ratio $\Gamma_{a}^{\text{Prim}}/\Gamma_{a}^{\text{Prim,asymp}}$, where $\Gamma^{\text{Prim}}_{a}$ is the ALP production rate in the Primakoff process given by Eq. \ref{['eq:ALP-total-production-rate']}, whereas $\Gamma_{a}^{\text{prim,asymp}}$ is the asymptotics given by Eq. \ref{['eq:ALP-production-rate-massless-asymptotics']}. Several ALP masses are considered. Right panel: the ratio $\Gamma_{a}\cdot (n_{a}^{\text{eq}}/n_{\gamma})/3H$, which controls whether the ALPs may enter thermal equilibrium at the given temperature $T$. The value of the ALP coupling is fixed by requiring the lifetime to be $\tau_{a} = 0.1\,{\rm s}\xspace$. Independent of the ALP mass, the ratio is the highest at large temperatures (being driven by the Primakoff process), then smoothly decreases, reaches a minimum, and starts increasing (being driven by the inverse ALP decay rate), asymptotically reaching $\tau_{a}^{-1}$.
• Figure 5: The ALP mass (left panel) and ALP lifetime (right panel) dependence of the ALP abundance $Y_{a} \equiv (n_{a}/s)|(T = 20\,{\rm MeV}\xspace)$, assuming different values of the late reheating temperature $T_{\rm reh}\xspace$. The gray dashed line shows the abundance if assuming the ALPs were in thermal equilibrium.