Primordial Magnetic Helicity Constraints from WMAP Nine-Year Data
  If a primordial magnetic field in the universe has non-zero helicity, the
violation of parity symmetry results in non-zero correlations between cosmic
microwave background temperature and B-mode polarization. In this paper we
derive approximations to the relevant microwave background power spectra
arising from a helical magnetic field. Using the cross-power spectrum between
temperature and B-mode polarization from the WMAP nine-year data, we set a 95\%
confidence level upper limit on the helicity amplitude to be 10 nG$^2$ Gpc for
helicity spectral index $n_H = -1.9$, for a cosmological magnetic field with
effective field strength of 3 nG and a power-law index $n_B = -2.9$ near the
scale-invariant value. Future microwave background polarization maps with
greater sensitivity will be able to detect the helicity of an inflationary
magnetic field well below the maximum value allowed by microwave background
constraints on the magnetic field amplitude.
