Cosmological Bound on the QCD Axion Mass, Redux

Abstract: We revisit the joint constraints in the mixed hot dark matter scenario in which both thermally produced QCD axions and relic neutrinos are present. Upon recomputing the cosmological axion abundance via recent advances in the literature, we improve the state-of-the-art analyses and provide updated bounds on axion and neutrino masses. By avoiding approximate methods, such as the instantaneous decoupling approximation, and limitations due to the limited validity of the perturbative approach in QCD that forced to artificially divide the constraints from the axion-pion and the axion-gluon production channels, we find robust and self-consistent limits. We investigate the two most popular axion frameworks: KSVZ and DFSZ. From Big Bang Nucleosynthesis (BBN) light element abundances data we find for the KSVZ axion $\Delta N_{\rm eff}<0.31$ and an axion mass bound $m_a < 0.53 $ eV (i.e., a bound on the axion decay constant $f_a > 1.07 \times 10^7$ GeV) both at $95\%$ CL. These BBN bounds are improved to $\Delta N_{\rm eff}<0.14$ and $m_a< 0.16$ eV ($f_a > 3.56 \times 10^7$ GeV) if a prior on the baryon energy density from Cosmic Microwave Background (CMB) data is assumed. When instead considering cosmological observations from the CMB temperature, polarization and lensing from the Planck satellite combined with large scale structure data we find $\Delta N_{\rm eff}<0.23$, $m_a< 0.28$ eV ($f_a > 2.02 \times 10^7$ GeV) and $\sum m_\nu < 0.16$ eV at $95\%$ CL. This corresponds approximately to a factor of $5$ improvement in the axion mass bound with respect to the existing limits. Very similar results are obtained for the DFSZ axion. We also forecast upcoming observations from future CMB and galaxy surveys, showing that they could reach percent level errors for $m_a\sim 1$ eV.