The CMBR ISW and HI 21 cm cross-correlation angular power spectrum

The late-time growth of large scale structures is imprinted in the CMBR anisotropy through the Integrated Sachs Wolfe (ISW) effect. This is perceived to be a very important observational probe of dark energy. Future observations of redshifted 21-cm radiation from the cosmological neutral hydrogen (HI) distribution hold the potential of probing the large scale structure over a large redshift range. We have investigated the possibility of detecting the ISW through cross-correlations between the CMBR anisotropies and redshifted 21-cm observations. Assuming that the HI traces the dark matter, we find that the ISW-HI cross-correlation angular power spectrum at an angular multipole l is proportional to the dark matter power spectrum evaluated at the comoving wave number l/r, where r is the comoving distance to the redshift from which the HI signal originated. The amplitude of the cross-correlation signal depends on parameters related to the HI distribution and the growth of cosmological perturbations. However, the cross-correlation is extremely weak as compared to the CMBR anisotropies and the predicted HI signal. Even in an ideal situation, the cross-correlation signal is smaller than the cosmic variance and a statistically significant detection is not very likely