Chameleon-Photon Mixing in a Primordial Magnetic Field
  We consider the non-resonant mixing between photons and scalar ALPs with
masses much less than the plasma frequency along the path, with specific
reference to the chameleon scalar field model. The mixing would alter the
intensity and polarization state of the cosmic microwave background (CMB)
radiation. We find that the average modification to the CMB polarization modes
is negligible. However the average modification to the CMB intensity spectrum
is more significant and we compare this to high precision measurements of the
CMB monopole made by the far infrared absolute spectrophotometer (FIRAS) on
board the COBE satellite. The resulting 95\% confidence limit on the
scalar-photon conversion probability in the primordial field (at 100 GHz) is P
< 2.6x10^{-2}. This corresponds to a degenerate constraint on the photon-scalar
coupling strength, g, and the magnitude of the primordial magnetic field.
Taking the upper bound on the strength of the primordial magnetic field derived
from the CMB power spectra, B < 5.0x10^{-9}G, this would imply an upper bound
on the photon-scalar coupling strength in the range g < 7.14x10^{-13}GeV^{-1}
to g < 9.20x10^{-14}GeV^{-1}, depending on the power spectrum of the primordial
magnetic field.
