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The nature of dark matter is an unsolved cosmological problem and axions are one of the weakly interacting cold dark matter candidates. Axions or ALPs (Axion-like particles) are pseudo-scalar bosons predicted by beyond-standard model theories. The weak coupling of ALPs with photons leads to the conversion of CMB photons to ALPs in the presence of a transverse magnetic field. If they have the same mass as the effective mass of a photon in a plasma, the resonant conversion would cause a polarized spectral distortion leading to temperature fluctuations with the distortion spectrum. The probability of resonant conversion depends on the properties of the cluster such as the magnetic field, electron density, and its redshift. We show that this kind of conversion can happen in numerous unresolved galaxy clusters up to high redshifts, which will lead to a diffused polarised anisotropy signal in the microwave sky. The spectrum of the signal and its shape in the angular scale will be different from the lensed CMB polarization signal. This new polarised distortion spectrum will be correlated with the distribution of clusters in the universe and hence, with the large-scale structure. The spectrum can then be probed using its spectral and spatial variation with respect to the CMB and various foregrounds. An SNR of 4. 36 and 93. 87 are possible in the CMB-S4 145 GHz band and CMB-HD 150 GHz band respectively for a photon-ALPs coupling strength of g₀ = ₁₀^-₁₂ \, GeV^{-1} using galaxy clusters beyond redshift z = 1. The same signal would lead to additional RMS fluctuations of 7. 5 10^-2 \, K at 145 GHz. In the absence of any signal, future CMB experiments such as Simons Observatory (SO), CMB-S4, and CMB-HD can put constraints on coupling strength better than current bounds from particle physics experiment CERN Axion Solar Telescope (CAST).
Mehta et al. (Tue,) studied this question.