http://arxiv.org/abs/1402.3293

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 a $\sim 5\%$ accuracy, even though the bispectrum can already deviate from leading-order perturbation theory by more than $30\%$. We further show that the relation extends up to nonlinear scales, $k \sim 1.0\,h\,\mathrm{Mpc}^{-1}$, within an accuracy of $\sim 10\%$.

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T. Nishimichi and P. Valageas
Mon, 17 Feb 14
21/37