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.
