HI Fluctuations at Large Redshifts: I--Visibility correlation

We investigate the possibility of probing the large scale structure in the universe at large redshifts by studying fluctuations in the redshifted 1420 MHz emission from the neutral hydrogen (HI) at early epochs. The neutral hydrogen content of the universe is known from absorption studies for z<4.5. The HI distribution is expected to be inhomogeneous in the gravitational instability picture and this inhomogeneity leads to anisotropy in the redshifted HI emission. The best hope of detecting this anisotropy is by using a large low-frequency interferometric instrument like the Giant Meter-Wave Radio Telescope (GMRT). We calculate the visibility correlation function <V_nu(u) V_nu'(u)> at two frequencies nu and nu' of the redshifted HI emission for an interferometric observation. In particular we give numerical results for the two GMRT channels centered around nu =325 and 610 MHz from density inhomogeneity and peculiar velocity of the HI distribution. The visibility correlation is ~10^-9 to 10^-10 Jy^2. We calculate the signal-to-noise for detecting the correlation signal in the presence of system noise and show that the GMRT might detect the signal for integration times ~ 100 hrs. We argue that the measurement of visibility correlation allows optimal use of the uncorrelated nature of the system noise across baselines and frequency channels.