Axion production and CMB spectral distortion in cosmological tangled magnetic field

Abstract

Axion production due to photon-axion mixing in tangled magnetic field(s) prior to recombination epoch and magnetic field damping can generate cosmic microwave background (CMB) spectral distortions. In particular, contribution of both processes to CMB $\mu$ distortion in the case of resonant photon-axion mixing is studied. Assuming that magnetic field power spectrum is approximated by a power law $P_B(k)\propto k^n$ with spectral index $n$, it is shown that for magnetic field cut-off scales $172.5$ pc $\le {\lambda }_B\le 4\times 10^3$ pc, axion contribution to CMB $\mu$ distortion is subdominant in comparison with magnetic field damping in the cosmological plasma. Using COBE upper limit on $\mu$ and for magnetic field scale ${\lambda }_B\simeq 415$ pc, weaker limit in comparison with other studies on the magnetic field strength ($B_0\le 8.5\times 10^{-8}$ G) up to a factor 10 for the DFSZ axion model and axion mass $m_a\ge 2.6\times 10^{-6}$ eV is found. A forecast for the expected sensitivity of PIXIE/PRISM on $\mu$ is also presented.

Typos corrected. Requested by the referee some additional text has been added. Minor changes. Version to be published at EPJ C

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