2014/02/28 by Takahiro Nishimichi, Patrick Valageas
Mathematics · Physics and Astronomy · #Bispectrum #Cosmology and Gravitation Theories #Domain (mathematical analysis) #Mathematical analysis #Mathematical physics #Mathematics #Omega #Order (exchange) #Perturbation theory (quantum mechanics) #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Spectral density #Statistics #Stellar, planetary, and galactic studies #astro-ph.CO
paper · pdf · doi:10.1103/physrevd.90.023546
published as Phys. Rev. D 90, 023546 (2014) · 14 pages, 15 figures, added Sec. III E and Appendixes, matched to PRD published version
openalex publication_date 2014/07/31 · arxiv created 2014/08/04 · arxiv updated 2014/08/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 (\ensuremathℓ+n)-point and n-point polyspectra, where one averages over the angles of \ensuremathℓ soft modes. This relation depends on two wave numbers, k^\ensuremath' in the soft domain and k in the hard domain. We show that it holds up to a good accuracy, when k^\ensuremath'/k\ensuremath≪1 and k^\ensuremath' is in the linear regime, while the hard mode k goes from linear (0.1h Mpc^\ensuremath-1) to nonlinear (1.0h Mpc^\ensuremath-1) scales. On scales k\ensuremath\lesssim0.4h Mpc^\ensuremath-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 \ensuremath∼7% at k\ensuremath∼1.0h Mpc^\ensuremath-1 at z=0.35. We show that this can be explained partly by the breakdown of the approximation \mathrm\ensuremathΩm/f2\ensuremath≃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.