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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 α  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 α  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 Ly α  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 Ly α  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.

Cross‐correlation of the H i 21‐cm signal and Lyα forest: a probe of cosmology