Probing primordial non-Gaussianity: The 3D Bispectrum of Ly-alpha forest
  and the redshifted 21-cm signal from the post reionization epoch
  We explore possibility of using the three dimensional bispectra of the
Ly-alpha forest and the redshifted 21-cm signal from the post-reionization
epoch to constrain primordial non-Gaussianity. Both these fields map out the
large scale distribution of neutral hydrogen and maybe treated as tracers of
the underlying dark matter field. We first present the general formalism for
the auto and cross bispectrum of two arbitrary three dimensional biased tracers
and then apply it to the specific case. We have modeled the 3D Ly-alpha
transmitted flux field as a continuous tracer sampled along 1D skewers which
corresponds to quasars sight lines. For the post reionization 21-cm signal we
have used a linear bias model. We use a Fisher matrix analysis to present the
first prediction for bounds on f_{NL} and the other bias parameters using the
three dimensional 21-cm bispectrum and other cross bispectra. The bounds on
f_{NL} depend on the survey volume, and the various observational noises. We
have considered a BOSS like Ly-alpha survey where the average number density of
quasars \bar{n} = 10^{-3} Mpc^{-2} and the spectra are measured at a 2-sigma
level. For the 21-cm signal we have considered a 4000 hrs observation with a
futuristic SKA like radio array. We find that bounds on f_{NL} obtained in our
analysis (6 < \Delta f_{NL} < 65) is competitive with CMBR and galaxy surveys.
We also find that by combining the various cross-bispectrum estimators it is
possible to constrain f_{NL} at a level \Delta f_{NL} ~ 4.7. For the
equilateral and orthogonal template we obtain \Delta f_{NL}^{equ}~17 and \Delta
f_{NL}^{orth}~13 respectively for the combined estimator. This shall be
important in the quest towards understanding the mechanism behind the
generation of primordial perturbations.
