Constraining Primordial Magnetic Fields by CMB Photon-Graviton
  Conversion
  We revisit the method of using the photon-graviton conversion mechanism in
the presence of the external magnetic field to probe small-scale primordial
magnetic fields that may exist between the last scattering surface and present.
Specifically, we investigate impacts on the conversion efficiency due to the
presence of matter, including the plasma collective effect and the atomic
polarizability. In general, these effects tend to reduce the conversion
probability. Under this more realistic picture and based on the precision of
COBE's measurement of CMB (cosmic microwave background) blackbody spectrum, we
find an upper bound for the primordial magnetic field strength, B < 30G, at the
time of recombination. Although at present the bound based on the
photon-graviton conversion mechanism is not as tight as that obtained by the
direct use of CMB temperature anisotropy, it nevertheless provides an important
independent constraint on primordial magnetic fields and at epochs in addition
to the recombination. The bound can be significantly improved if the CMB
blackbody spectrum measurement becomes more precise in future experiments such
as PIXIE.
