Abstract:
We investigate the possibility of detecting the 3D cross correlation power spectrum of the Ly-α forest and HI 21 cm signal from the post reionization epoch. {The cross-correlation signal is directly dependent on the dark matter power spectrum and is sensitive to the 21-cm brightness temperature and Ly-α forest biases. These bias parameters dictate the strength of anisotropy in redshift space.} We find that the cross-correlation power spectrum can be detected using 400 hrs observation with SKA-mid (phase 1) and a futuristic BOSS like experiment with a quasar (QSO) density of 30 deg−2 at a peak SNR of 15 for a single field experiment at redshift z = 2.5. on large scales using the linear bias model. We also study the possibility of constraining various bias parameters using the cross power spectrum. We find that with the same experiment 1 σ {conditional errors} on the 21-cm linear redshift space distortion parameter βT and βF corresponding to the Ly-α forest are ∼ 2.7 % and ∼ 1.4 % respectively for 01 independent pointings of the SKA-mid (phase 1). This prediction indicates a significant improvement over existing measurements. We claim that the detection of the 3D cross correlation power spectrum will not only ascertain the cosmological origin of the signal in presence of astrophysical foregrounds but will also provide stringent constraints on large scale HI biases. This provides an independent probe towards understanding cosmological structure formation.