GMRT observation of neutral atomic hydrogen gas in the COSMOS field at
  $z \sim 0.37$
  We present the results of HI spectral stacking analysis of Giant Metrewave
Radio Telescope (GMRT) observations targeting the COSMOS field. The GMRT data
cube contains 474 field galaxies with redshifts known from the zCOSMOS-bright
10k catalogue. Spectra for the galaxies are co-added and the stacked spectrum
allows us to make a $\sim 3\sigma$ measurement of the average HI mass. Using
this average HI mass along with the integral optical $B$-band luminosity of the
galaxies and the luminosity density of the COSMOS field, a volume normalisation
is applied to obtain the cosmic HI mass density ($\Omega_{\rm HI}$). We find a
cosmic HI mass density of $\Omega_{\rm HI}$ = (0.42 $\pm$ 0.16) $\times$
10$^{-3}$ at $z \sim 0.37$, which is the highest-redshift measurement of
$\Omega_{\rm HI}$ ever made using HI spectral stacking. The value we obtained
for $\Omega_{\rm HI}$ at $z \sim 0.37$ is consistent with that measured from
large blind 21-cm surveys at $z = 0$ as well as measurements from other HI
stacking experiments at lower redshifts. Our measurement in conjunction with
earlier measurements indicates that there has been no significant evolution of
HI gas abundance over the last 4 Gyr. A weighted mean of $\Omega_{\rm HI}$ from
all 21-cm measurements at redshifts $z \lesssim 0.4$ gives $\Omega_{\rm HI}$ =
(0.35 $\pm$ 0.01) $\times$ 10$^{-3}$. The $\Omega_{\rm HI}$ measured (from HI
21-cm emission measurements) at $z \lesssim 0.4$ is however approximately half
that measured from Damped Lyman-$\alpha$ Absorption (DLA) systems at $z \gtrsim
2$. Deeper surveys with existing and upcoming instruments will be critical to
understand the evolution of $\Omega_{\rm HI}$ in the redshift range
intermediate between $z \sim 0.4$ and the range probed by DLA observations.
