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

Abstract

We explore possibility of using the three dimensional bispectra of the Ly-α 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-α 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 fNL and the other bias parameters using the three dimensional 21-cm bispectrum and other cross bispectra. The bounds on fNL depend on the survey volume, and the various observational noises. We have considered a BOSS like Ly-α survey where the average number density of quasars bar n = 10−3Mpc−2 and the spectra are measured at a 2-σ 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 fNL obtained in our analysis (6 ⩽ ΔfNL ⩽ 65) is competitive with CMBR and galaxy surveys and may prove to be an important alternative approach towards constraining primordial physics using future data sets. Further, we have presented a hierarchy of power of the bispectrum-estimators towards detecting the fNL. Given the quality of the data sets, one may use this method to optimally choose the right estimator and thereby provide better constraints on fNL. We also find that by combining the various cross-bispectrum estimators it is possible to constrain fNL at a level ΔfNL ∼ 4.7. For the equilateral and orthogonal template we obtain ΔfNLequ ∼ 17 and ΔfNLorth ∼ 13 respectively for the combined estimator. This shall be important in the quest towards understanding the mechanism behind the generation of primordial perturbations.