Redshift-space equal-time angular-averaged consistency relations of the gravitational dynamics

Abstract

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, $k=0.2h{\mathrm{Mpc}}^{-1}$, it still holds within the statistical accuracy of idealized simulations of volume $\sim 8h^{-3}{\mathrm{Gpc}}^3$ without shot-noise error.

19 pages, 4 figures. arXiv admin note: text overlap with arXiv:1311.4286

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