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 < Δf_{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 Δf_{NL} ~ 4.7. For the equilateral and orthogonal template we obtain Δf_{NL}^{equ}~17 and Δf_{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.