Hot Axions and the $H_0$ tension

TL;DR

The paper examines how hot axions produced by scattering and decay of heavy leptons near the QCD phase transition contribute an extra radiation density parameterized by $ΔN_{\rm eff}$. It derives the axion production rates from both diagonal and off-diagonal lepton currents, solves the Boltzmann equation for the axion abundance, and maps this to $ΔN_{\rm eff}$ with both analytic aides and numerical results. Using Planck 2018 and BAO data with priors tied to axion–lepton couplings, it finds $ΔN_{\rm eff}$ can reach up to about 0.6 for muon scattering, 0.3 for tau decays or scatterings, and 0.2 for tau scatterings, which can modestly alleviate the $H_0$ tension within $Λ$CDM. However, current cosmological data still constrain $ΔN_{\rm eff}$ to be small, so the tension is not fully resolved, though certain priors and channels can reduce it to around $2.75\sigma$. The work highlights hot axions as a testable cosmological component and motivates future CMB experiments to probe $ΔN_{\rm eff}$ with higher precision, potentially revealing axion physics tied to heavy-lepton couplings.

Abstract

Scattering and decay processes of thermal bath particles involving heavy leptons can dump hot axions in the primordial plasma around the QCD phase transition. We compute their relic density, parameterized by an effective number $ΔN_{\rm eff}$ of additional neutrinos. For couplings allowed by current bounds, production via scattering yields $ΔN_{\rm eff} \lesssim 0.6$ and $ΔN_{\rm eff} \lesssim 0.2$ for the cases of muon and tau, respectively. Flavor violating tau decays to a lighter lepton plus an axion give $ΔN_{\rm eff} \lesssim 0.3$. Such values of $ΔN_{\rm eff}$ can alleviate the tension between the direct local measurement of the Hubble constant $H_0$ and the inferred value from observations of the Cosmic Microwave Background, assuming $Λ$CDM. We analyze present cosmological data from the Planck collaboration and baryon acoustic oscillations with priors given in terms of the axion-lepton couplings. For axions coupled to muons, the tension can be alleviated below the 3$σ$ level. Future experiments will measure $ΔN_{\rm eff}$ with higher precision, providing an axion discovery channel and probing the role of hot axions in the $H_0$ tension.

Figures (8)

• Figure 1: Numerical solutions for an axion coupled to the $\tau$ for both scattering (red) and decay (blue). The dashed black line represents the axion comoving equilibrium number density.
• Figure 2: Contribution to $N_{\rm eff}$ from muon (blue) and tau (red) scattering as a function of $c_\ell/f$. Decays are possible for off-diagonal couplings; we show only results for tau decays (magenta), which are the only allowed ones in the above range for $c_{\ell \ell^\prime}/f$. Each process is shown as a band, parameterizing the uncertainty in the number of relativistic degrees of freedom: the straight line $g_*$ is taken from Laine:2006cp and the dashed line from Borsanyi:2016ksw. We also show the analytical expectation, $N_{\rm eff} \propto f^{-8/3}$, for non-thermalized axions. The orange bands represent the forecasted sensitivities for future CMB experiments Abazajian:2016yjj.
• Figure 3: Posterior distribution of $\log_{10}(f/c_\ell)$ obtained assuming a $\Lambda$CDM+$\Delta N_\text{eff}$ model with flat priors in $\Delta N_\text{eff}$ and considering only the values of $\Delta N_\text{eff}$ accessible for each case (see Fig. \ref{['figura']}). We show results for axion production via $\mu$ scatterings (blue), $\tau$ scattering (red) and $\tau$ decays (magenta). We do not show the parameter space corresponding to $f/c_{\tau \ell^\prime} < 3 \times 10^6 \, {\rm GeV}$ since it is ruled out by the constraints discussed in Sec. \ref{['Lag']}. Solid and dashed lines assume $g_*$ from Refs. Laine:2006cp and Borsanyi:2016ksw, respectively. The full Planck angular power spectra and BAO data were used in all cases.
• Figure 4: 68% and 95% confidence level regions in the $(H_0, \Delta N_\text{eff})$ plane for hot axions assuming axion production via decays and scattering with tau (upper left and upper right panels, respectively) and scattering with muons (lower left panel). We consider three different priors (shown in different colors), all of them flat in $\log_{10}(f/c_{\ell})$ but with different maximum values of $f/c_{\ell}$, as indicated in the legend. We also show the constraints (bottom right panel) assuming a standard $\Lambda$CDM+$\Delta N_\text{eff}$ model with flat priors in $\Delta N_\text{eff}$ > 0 . The full Planck angular power spectra and BAO data were used in all cases. Note the change of scale in the horizontal axis in each panel.
• Figure 5: Constraint on $f/c_\mu$ as a function of the SN temperature.