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

Understand

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.