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Testing the equal-time angular-averaged consistency relation of the gravitational dynamics in N-body simulations

Abstract

We explicitly test the equal-time consistency relation between the angular-averaged bispectrum and the power spectrum of the matter density field, employing a large suite of cosmological NN-body simulations. This is the lowest-order version of the relations between (+n)(\ell+n)-point and nn-point polyspectra, where one averages over the angles of \ell soft modes. This relation depends on two wave numbers, kk' in the soft domain and kk in the hard domain. We show that it holds up to a good accuracy, when k/k1k'/k\ll 1 and kk' is in the linear regime, while the hard mode kk goes from linear (0.1hMpc10.1\,h\mathrm{Mpc}^{-1}) to nonlinear (1.0hMpc11.0\,h\mathrm{Mpc}^{-1}) scales. On scales k0.4hMpc1k\lesssim 0.4\,h\mathrm{Mpc}^{-1}, we confirm the relation within the statistical error of the simulations (typically a few percent depending on the wave number), even though the bispectrum can already deviate from leading-order perturbation theory by more than 30%30\%. We further examine the relation on smaller scales with higher resolution simulations. We find that the relation holds within the statistical error of the simulations at z=1z=1, whereas we find deviations as large as 7%\sim 7\% at k1.0hMpc1k \sim 1.0\,h\mathrm{Mpc}^{-1} at z=0.35z=0.35. We show that this can be explained partly by the breakdown of the approximation Ωm/f21\Omega_\mathrm{m}/f^2\simeq1 with supplemental simulations done in the Einstein-de Sitter background cosmology. We also estimate the impact of this approximation on the power spectrum and bispectrum.Comment: 14 pages, 15 figures, added Sec. III E and Appendixes, matched to PRD published versio

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