Predictions for BAO distance estimates from the cross-correlation of the
  Lyman-alpha forest and redshifted 21-cm emission
  We investigate the possibility of using the cross-correlation of the
Lyman-alpha forest and redshifted 21-cm emission to detect the baryon acoustic
oscillation (BAO). The standard Fisher matrix formalism is used to determine
the accuracy with which it will be possible to measure cosmological distances
using this signal. Earlier predictions indicate that it will be possible to
measure the dilation factor D_V with 1.9 % accuracy at z=2.5 from the BOSS
Lyman-alpha forest auto-correlation. In this paper we investigate if it is
possible to improve the accuracy using the cross-correlation.
  We use a simple parametrization of the Lyman-alpha forest survey which very
loosely matches some properties of BOSS and predicts delta D_V/D_V = 2.0 % for
the auto-correlation at z=2.5. For the redshifted 21-cm observations we
consider individual antennas of size 2 m * 2 m distributed such that the
baselines within 250 m are uniformly sampled. It is assumed that the
observations span z=2 to 3 and covers the 10,000 deg^2 sky coverage of BOSS. We
find that for 2 years of observation with an array of 2,000 antennas, the
cross-correlation is 1.7 times more sensitive than the Lyman-alpha forest
auto-correlation. The cross-correlation is 2.7 times more sensitive than the
auto-correlation if we have 4,000 antennas and 4 years of observation. In
conclusion, we find that it is possible to significantly increase the accuracy
of the distance estimates by considering the cross-correlation signal.
