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

Takahiro Nishimichi (1) , Patrick Valageas (2)

1 IAP - Institut d'Astrophysique de Paris
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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 (0.1h ^Mpc-1) to nonlinear (1.0h Mpc-¹) scales. On scales k ≲0.4h ^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 ∼7% at k ∼1.0h ^Mpc-1 at z =0.35. We show that this can be explained partly by the breakdown of the approximation Ω_m/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.

Keywords: 98.80.-k; Cosmology; Astrophysics - Cosmology and Nongalactic Astrophysics

Domains: Sciences of the Universe [physics]

Takahiro Nishimichi, Patrick Valageas. Testing the equal-time angular-averaged consistency relation of the gravitational dynamics in N-body simulations. Physical Review D, 2014, 90, pp.023546. ⟨10.1103/PhysRevD.90.023546⟩. ⟨insu-03645358⟩