Constraining large scale HI bias using redshifted 21-cm signal from the
  post-reionization epoch
  In the absence of complex astrophysical processes that characterize the
reionization era, the 21-cm emission from neutral hydrogen (HI) in the
post-reionization epoch is believed to be an excellent tracer of the underlying
dark matter distribution. Assuming a background cosmology, it is modelled
through (i) a bias function b(k,z), which relates HI to the dark matter
distribution and (ii) a mean neutral fraction (x_{HI}) which sets its
amplitude. In this paper, we investigate the nature of large scale HI bias. The
post-reionization HI is modelled using gravity only N-Body simulations and a
suitable prescription for assigning gas to the dark matter halos. Using the
simulated bias as the fiducial model for HI distribution at z\leq 4, we have
generated a hypothetical data set for the 21-cm angular power spectrum (C_{l})
using a noise model based on parameters of an extended version of the GMRT. The
binned C_{l} is assumed to be measured with SNR \gtrsim 4 in the range 400 \leq
l \leq 8000 at a fiducial redshift z=2.5. We explore the possibility of
constraining b(k) using the Principal Component Analysis (PCA) on this
simulated data. Our analysis shows that in the range 0.2 < k < 2 Mpc^{-1}, the
simulated data set cannot distinguish between models exhibiting different k
dependences, provided 1 \lesssim b(k) \lesssim 2 which sets the 2-sigma limits.
This justifies the use of linear bias model on large scales. The largely
uncertain x_{HI} is treated as a free parameter resulting in degradation of the
bias reconstruction. The given simulated data is found to constrain the
fiducial x_{HI} with an accuracy of \sim 4% (2-sigma error). The method
outlined here, could be successfully implemented on future observational data
sets to constrain b(k,z) and x_{HI} and thereby enhance our understanding of
the low redshift Universe.
