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 Lyα 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 Lyα 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 3σ 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 Lyα forest survey. Assuming that the spectra have S/N ∼ 5 in pixels of length 44 km s−1, we find that a 5σ 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 Lyα 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.