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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 (+n)(\ell+n)- and nn-point polyspectra of the cosmological matter density field. Focusing on the case of =1\ell=1 large-scale mode and nn 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 NN-body simulations, we find that our squeezed bispectrum relation is valid to better than 20%20\% up to 1h1hMpc1^{-1}, for both the monopole and quadrupole at z=0.35z=0.35, in a Λ\LambdaCDM 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%20\% up to 1h1hMpc1^{-1}, at z=0.35z=0.35 for the monopole. On larger scales, k=0.2hMpc1k = 0.2 h\mathrm{Mpc}^{-1}, it still holds within the statistical accuracy of idealized simulations of volume 8h3Gpc3\sim8h^{-3}\mathrm{Gpc}^3 without shot-noise error.Comment: 19 pages, 4 figures. arXiv admin note: text overlap with arXiv:1311.428

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    Last time updated on 19/05/2022
    Last time updated on 19/05/2022