Beyond thermal approximations: Precise cosmological bounds on Axion-Like Particles

TL;DR

The paper develops a fully phase-space-based cosmological analysis of light ALPs coupled to leptons or photons, solving the momentum-dependent Boltzmann equation to obtain the exact ALP PSD and tracking its impact on observables through a Boltzmann solver. By performing joint MCMC fits to Planck, ACT, SPT, and BBN data (with DESI BAO) and exploring priors, the authors derive leading bounds: for ALP-lepton couplings, $f_a>\{1.63\times10^6, 9.41\times10^6, 8.06\times10^4\}$ GeV for $e,\mu,\tau$ respectively, and for ALP-photon coupling, $g_{a\gamma}<1.98\times10^{-8}$ GeV$^{-1}$, with DESI mildly relaxing the limits. They also forecast future improvements for LiteBIRD+Simons Observatory and LiteBIRD+CMB-HD, highlighting significant gains in the $\tau$ channel and for Primakoff-mediated bounds, while showing the critical role of exact PSD treatment for robust constraints. A prior-sensitivity analysis favors a $\Delta N_{\rm eff}$-based sampling to minimize prior volume effects, and comparisons with thermal spectra quantify the impact of non-thermal distortions on the inferred bounds. Overall, the work demonstrates that precise phase-space treatment is essential for robust cosmological bounds on ALP interactions and guides expectations for upcoming CMB surveys.

Abstract

We derive updated cosmological bounds on light axion-like particles (ALPs) coupled to leptons or photons, using a full phase-space treatment of their production from the primordial thermal plasma. The ALP phase-space distribution, obtained by solving the momentum-dependent Boltzmann equation for the relevant production processes, is consistently propagated into the computation of cosmological observables, allowing us to assess the impact of non-thermal spectral distortions on the effective number of relativistic species, $ΔN_{\rm eff}$. Using state-of-the-art measurements of the cosmic microwave background from Planck, the Atacama Cosmology Telescope, and the South Pole Telescope, complemented with Big Bang Nucleosynthesis determinations of primordial deuterium and helium abundances, we obtain the following 95\% credible limits on the ALP decay constant: $f_a > 1.63 \times 10^6 \, {\rm GeV}$, $9.41 \times 10^6 \, {\rm GeV}$ and $8.06 \times 10^4 \, {\rm GeV}$ for ALPs coupled to electrons, muons and taus, respectively. For the ALP-photon coupling we find $g_{aγ} < 1.98 \times 10^{-8} \, {\rm GeV}^{-1}$. Including baryon acoustic oscillation data from the Dark Energy Spectroscopic Instrument mildly relaxes the constraints, in line with previous analyses of extra relativistic degrees of freedom. Finally, we present forecasts for the LiteBIRD$+$Simons Observatory and LiteBIRD$+$CMB-HD configurations, discussing the importance of an exact phase-space treatment for robust cosmological bounds on ALP interactions.

Figures (12)

• Figure 1: Feynman diagrams for ALP production via interactions with leptons. From left to right: lepton pair annihilation ($t$ and $u$-channel) and Compton-like scattering ($s$ and $u$-channel).
• Figure 2: Left: collision rate for production of ALPs through leptonic interactions with electrons (blue), muons (orange), and taus (green), as a function of the temperature of the primordial plasma. The curves correspond to two fixed values of the momentum, $k/T = 0.1$ (solid) and $k/T = 10$ (dashed). The ALP decay constant is set to $f_a = 10^5 \, {\rm GeV}$, with $c_\ell = 1$ by convention. The dot-dashed line denotes the Hubble expansion rate. Right: Exact ALP phase-space distributions for the electron channel (solid lines) compared with Bose-Einstein distributions with temperatures rescaled to yield the same $\Delta N_{\rm eff}$ (dashed lines), for different values of $f_a$. The lower sub-panel shows the difference between the exact and thermal distribution functions, quantified by the parameter $\delta_{\rm th}$ defined in eq. \ref{['eq:delta_th']}.
• Figure 3: $t$-channel diagram for Primakoff production of an ALP.
• Figure 4: Photon plasma mass, $m_\gamma$, as a function of the temperature of the primordial plasma. The orange markers denote values computed using eq. \ref{['eq:plasma_mass']}, including only leptons in the sum for $T \leq 100 \, {\rm MeV}$, and both leptons and quarks for $T \geq 1 \, {\rm GeV}$. The solid blue curve represents the smooth interpolation between these two regimes across the QCD phase transition epoch. The green dotted curve corresponds to the photon mass in a relativistic $e^+e^-$ plasma, $m_\gamma \simeq e T / 3$ (see, e.g., Carrington:1997sqBolz:2000fu). This is well recovered from our full expression of $m_\gamma$ for temperatures $m_e \ll T \ll m_\mu$.
• Figure 5: Left: collision term for Primakoff production of ALPs through scattering off electrons (blue), taus (green), and top quarks (brown), as a function of the temperature of the primordial plasma. The curves correspond to two fixed values of the momentum, $k/T = 0.1$ (solid) and $k/T = 10$ (dashed). The ALP-photon coupling is set to $g_{a\gamma} = 10^{-7} \, {\rm GeV}^{-1}$. Vertical dotted lines mark the corresponding fermion masses. The dot-dashed line denotes the Hubble expansion rate. Right: Exact ALP phase-space distributions produced via Primakoff interactions, including contributions from leptons and quarks for temperatures $T \geq 1\,\mathrm{GeV}$, for different values of the ALP–photon coupling $g_{a\gamma}$. Results are obtained by solving the momentum-dependent Boltzmann equation with the matrix element in eq. \ref{['eq:MatrixPrimakoff']}. As for the leptonic channels, we show for comparison the corresponding Bose-Einstein distributions (dashed lines) with temperatures rescaled to yield the same values of $\Delta N_{\rm eff}$.