Polarized anisotropic spectral distortions of the CMB: Galactic and extragalactic constraints on photon-axion conversion

We revisit the cosmological constraints on resonant and non-resonant conversion of photons to axions in the cosmological magnetic fields. We find that the constraints on photon-axion coupling and primordial magnetic fields are much weaker than previously claimed for low mass axion like particles with masses $m_{\rm a} \lesssim 5\times 10^{-13}\,\text{eV}$. In particular we find that the axion mass range $10^{-14}\,\text{eV} \le m_{\rm a} \le 5\times 10^{-13}\,\text{eV}$ is not excluded by the CMB data contrary to the previous claims. We also examine the photon-axion conversion in the Galactic magnetic fields. Resonant conversion in the large scale coherent Galactic magnetic field results in $100\%$ polarized anisotropic spectral distortions of the CMB for the mass range $10^{-13}\,\text{eV} \lesssim m_{\rm a} \lesssim 10^{-11}\,\text{eV}$. The polarization pattern traces the transverse to line of sight component of the Galactic magnetic field while both the anisotropy in the Galactic magnetic field and electron distribution imprint a characteristic anisotropy pattern in the spectral distortion. Our results apply to scalar as well as pseudoscalar particles. For conversion to scalar particles, the polarization is rotated by $90^{\circ}$ allowing us to distinguish them from the pseudoscalars. For $m_{\rm a} \lesssim 10^{-14} \,\text{eV}$ we have non-resonant conversion in the small scale turbulent magnetic field of the Galaxy resulting in anisotropic but unpolarized spectral distortion in the CMB. These unique signatures are potential discriminants against the isotropic and non-polarized signals such as primary CMB, and $\mu$ and $y$ distortions with the anisotropic nature making it accessible to experiments with only relative calibration like Planck, LiteBIRD, and CORE. We forecast for PIXIE as well as for these experiments using Fisher matrix formalism.