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 (ℓ+n)-point and n-point
polyspectra, where one averages over the angles of ℓ 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.Comment: 14 pages, 15 figures, added Sec. III E and Appendixes, matched to PRD
published versio