The Impact of Foregrounds on Redshift Space Distortion Measurements With
  the Highly-Redshifted 21 cm Line
  The highly redshifted 21 cm line of neutral hydrogen has become recognized as
a unique probe of cosmology from relatively low redshifts (z ~ 1) up through
the Epoch of Reionization (z ~ 8) and even beyond. To date, most work has
focused on recovering the spherically averaged power spectrum of the 21 cm
signal, since this approach maximizes the signal-to-noise in the initial
measurement. However, like galaxy surveys, the 21 cm signal is affected by
redshift space distortions, and is inherently anisotropic between the
line-of-sight and transverse directions. A measurement of this anisotropy can
yield unique cosmological information, potentially even isolating the matter
power spectrum from astrophysical effects. However, in interferometric
measurements, foregrounds also have an anisotropic footprint between the
line-of-sight and transverse directions: the so-called foreground "wedge".
Although foreground subtraction techniques are actively being developed, a
"foreground avoidance" approach of simply ignoring contaminated modes has
arguably proven most successful to date. In this work, we analyze the effect of
this foreground anisotropy in recovering the redshift space distortion
signature in 21 cm measurements at both high and intermediate redshifts. We
find the foreground wedge corrupts nearly all of the redshift space signal for
even the largest proposed EoR experiments (HERA and the SKA), making
cosmological information unrecoverable without foreground subtraction. The
situation is somewhat improved at lower redshifts, where the redshift-dependent
mapping from observed coordinates to cosmological coordinates significantly
reduces the size of the wedge. Using only foreground avoidance, we find that a
large experiment like CHIME can place non-trivial constraints on cosmological
parameters.
