Cross-correlation of the H I 21-cm signal and Ly alpha forest: a probe of cosmology

Separating the cosmological redshifted 21-cm signal from foregrounds is a major challenge. We present the cross-correlation of the redshifted 21-cm emission from neutral hydrogen (H i) in the post-reionization era with the Ly alpha forest as a new probe of the large-scale matter distribution in the redshift range z = 2-3 without the problem of foreground contamination. Though the 21-cm and the Ly alpha forest signals originate from different astrophysical systems, they are both expected to trace the underlying dark matter distribution on large scales. The multifrequency angular cross-correlation power spectrum estimator is found to be unaffected by the discrete quasar sampling, which only affects the noise in the estimate. We consider a hypothetical redshifted 21-cm observation in a single field of view 13 (FWHM) centred at z = 2.2, where the binned 21-cm angular power spectrum can be measured at a signal-to-noise ratio (S/N) of 3 Sigma or better across the range 500 < l < 4000. Keeping the parameters of the 21-cm observation fixed, we have estimated the S/N for the cross-correlation signal varying the quasar angular number density n of the Ly alpha forest survey. Assuming that the spectra have S/N similar to 5 in pixels of length 44 km s-1, we find that a 5 Sigma detection of the cross-correlation signal is possible at 600 < l < 2000 with n = 4 deg-2. This value of n is well within the reach of upcoming Ly alpha forest surveys. The cross-correlation signal will be a new, independent probe of the astrophysics of the diffuse intergalactic medium (IGM), the growth of structure and the expansion history of the Universe.