Redshift-space equal-time angular-averaged consistency relations of the gravitational dynamics
Résumé
We present the redshift-space generalization of the equal-time angular-averaged consistency relations between (ℓ+n )- and n -point polyspectra (i.e., the Fourier counterparts of correlation functions) of the cosmological matter density field. Focusing on the case of the ℓ=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 relation on the bispectrum in the squeezed limit (i.e., the limit where one wave number is much smaller than the other two) is valid to better than 20% up to 1 h Mpc-1 , for both the monopole and quadrupole at z =0.35 , in a Λ 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 1 h Mpc-1 , at z =0.35 for the monopole. On larger scales, k =0.2 h Mpc-1 , it still holds within the statistical accuracy of idealized simulations of volume ∼8 h-3Gpc3 without shot-noise error.
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