Testing the equal-time angular-averaged consistency relation of the
  gravitational dynamics in N-body simulations
  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 $(\ell+n)$-point and $n$-point
polyspectra, where one averages over the angles of $\ell$ 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 $k'/k\ll 1$ and
$k'$ is in the linear regime, while the hard mode $k$ goes from linear
($0.1\,h\mathrm{Mpc}^{-1}$) to nonlinear ($1.0\,h\mathrm{Mpc}^{-1}$) scales. On
scales $k\lesssim 0.4\,h\mathrm{Mpc}^{-1}$, 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 $30\%$. 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 $\sim 7\%$ at $k \sim 1.0\,h\mathrm{Mpc}^{-1}$ at
$z=0.35$. We show that this can be explained partly by the breakdown of the
approximation $\Omega_\mathrm{m}/f^2\simeq1$ 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.
