*** kSZ with SPECTROSCOPIC redshifts *** (Simone + Emmanuel)
This includes the "reconstructed" velocity and "pairwise momentum" estimators (which are equivalent). We show forecasts for a DESI-type spectroscopic galaxy survey with 20M galaxies over 14000 sq deg and assume full overlap. The results depend somewhat on the actual gas distribution around the tracer galaxies, whose determination is one of the goals of kSZ measurements. Here we assume to have no information on scales smaller than R_vir for a typical galaxy at z ~ 1, and the results are normalized to reproduce the actual S/N of current analyses.
*** kSZ with PHOTOMETRIC / NO redshifts information *** (Simone + Colin) useful for LSST (both clustering and lensing), WISE, SPHEREx, etc.
Here we follow http://arxiv.org/abs/1605.02722 and show forecasts for a few S4 configurations. Again the detailed numbers depend on the actual distribution of baryons on small scales (here assumed to trace the dark matter exactly on the scales of interest). Note that this method requires very good foregrounds cleaning and is much more sensitive to residual foreground than using "reconstructed velocities" or "pairwise momentum". The actual performance of this method is likely to be limited by component separation on the CMB side.
Here f_free is the free electron fraction of the tracer galaxies and parametrizes the kSZ amplitude. If f_free is known externally, this can be seen as a constrain on the growth factor with the same S/N.