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 N-body simulations. This is the lowest-order version of the relations between (?+n)-point and n-point polyspectra, where one averages over the angles of ? soft modes. This relation depends on two wave numbers, k′ in the soft domain and k in the hard domain. We show that it holds up to a good accuracy, when k′/k?1 and k′ is in the linear regime, while the hard mode k goes from linear (0.1hMpc-1) to nonlinear (1.0hMpc-1) scales. On scales k?0.4hMpc-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%. 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=1, whereas we find deviations as large as ∼7% at k∼1.0hMpc-1 at z=0.35. We show that this can be explained partly by the breakdown of the approximation Ωm/f2≃1 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. © 2014 American Physical Society.