Lensing Reconstruction Using Redshifted 21 Centimeter Fluctuations

We investigate the potential of second generation measurements of redshifted21 cm radiation from before and during the epoch of reionization (EOR) toreconstruct the matter density fluctuations along the line of sight. To do sowe generalize the quadratic methods developed for the Cosmic MicrowaveBackground (CMB) to 21 cm fluctuations. We show that the three dimensionalsignal can be decomposed into a finite number of line of sight Fourier modesthat contribute to the lensing reconstruction. Our formalism properly takesaccount of correlations along the line of sight and uses all the informationcontained in quadratic combinations of the signal. In comparison with the CMB,21 cm fluctuations have the disadvantage of a relatively scale invariantunlensed power spectrum which suppresses the lensing effect. The smallness ofthe lensing effect is compensated by using information from a range of observedredshifts. We estimate the size of experiments that are needed to measure thiseffect. With a square kilometer of collecting area and a maximal baseline of 3km one can achieve lensing reconstruction noise levels an order of magnitudebelow CMB quadratic estimator constraints at L=1000, and map the deflectionfield out to less then a tenth of a degree (L> 2000) within a season ofobservations on one field. Statistical lensing power spectrum detections willbe possible to sub-arcminute scales, even with the limited sky coverage thatcurrently conceived experiments have. One should be able to improve constraintson cosmological parameters by using this method. With larger collecting areasor longer observing times, one could probe arcminute scales of the lensingpotential and thus individual clusters. We address the effect that foregroundsmight have on lensing reconstruction with 21 cm fluctuations.Comment: 14 pages, 8 Figures, replaced to match version to appear in Ap