Redshift-space equal-time angular-averaged consistency relations of the
  gravitational dynamics
  We present the redshift-space generalization of the equal-time
angular-averaged consistency relations between $(\ell+n)$- and $n$-point
polyspectra of the cosmological matter density field. Focusing on the case of
$\ell=1$ large-scale mode and $n$ small-scale modes, we use an approximate
symmetry of the gravitational dynamics to derive explicit expressions that hold
beyond the perturbative regime, including both the large-scale Kaiser effect
and the small-scale fingers-of-god effects. We explicitly check these
relations, both perturbatively, for the lowest-order version that applies to
the bispectrum, and nonperturbatively, for all orders but for the
one-dimensional dynamics. Using a large ensemble of $N$-body simulations, we
find that our squeezed bispectrum relation is valid to better than $20\%$ up to
$1h$Mpc$^{-1}$, for both the monopole and quadrupole at $z=0.35$, in a
$\Lambda$CDM cosmology. Additional simulations done for the Einstein-de Sitter
background suggest that these discrepancies mainly come from the breakdown of
the approximate symmetry of the gravitational dynamics. For practical
applications, we introduce a simple ansatz to estimate the new derivative terms
in the relation using only observables. Although the relation holds worse after
using this ansatz, we can still recover it within $20\%$ up to $1h$Mpc$^{-1}$,
at $z=0.35$ for the monopole. On larger scales, $k = 0.2 h\mathrm{Mpc}^{-1}$,
it still holds within the statistical accuracy of idealized simulations of
volume $\sim8h^{-3}\mathrm{Gpc}^3$ without shot-noise error.
