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

Probing primordial non-Gaussianity: The 3D Bispectrum of Ly-alpha forest and the redshifted 21-cm signal from the post reionization epoch