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

Abstract

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, $k^{\prime }$ in the soft domain and $k$ in the hard domain. We show that it holds up to a good accuracy, when $k^{\prime }/k\ll 1$ and $k^{\prime }$ is in the linear regime, while the hard mode $k$ goes from linear ($0.1h{\mathrm{Mpc}}^{-1}$) to nonlinear ($1.0h{\mathrm{Mpc}}^{-1}$) scales. On scales $k\lesssim 0.4h{\mathrm{Mpc}}^{-1}$, 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 $k\sim 1.0h{\mathrm{Mpc}}^{-1}$ at $z=0.35$. We show that this can be explained partly by the breakdown of the approximation ${\Omega }_{\mathrm{m}}/f^2\simeq 1$ 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.

14 pages, 15 figures, added Sec. III E and Appendixes, matched to PRD published version

References in corpus (8)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe
• Single-Field Consistency Relations of Large Scale Structure. Part III: Test of the Equivalence Principle
• Consequences of Symmetries and Consistency Relations in the Large-Scale Structure of the Universe for Non-local bias and Modified Gravity
• Chasing the non-linear evolution of matter power spectrum with numerical resummation method: solution of closure equations
• Angular averaged consistency relations of large-scale structures
• Kinematic consistency relations of large-scale structures

Cited by in corpus (13)

• The angle-averaged squeezed limit of nonlinear matter N-point functions
• Is There Scale-Dependent Bias in Single-Field Inflation?
• Principal Shapes and Squeezed Limits in the Effective Field Theory of Large Scale Structure
• K-mouflage effects on clusters of galaxies
• The Integrated Bispectrum and Beyond
• A non-perturbative test of consistency relations and their violation
• Squeezing $f_{\mathrm{NL}}$ out of the matter bispectrum with consistency relations
• On Soft Limits of Large-Scale Structure Correlation Functions
• Consistency relations for large scale structures with primordial non-Gaussianities
• Non-zero density-velocity consistency relations for large scale structures
• Redshift-space equal-time angular-averaged consistency relations of the gravitational dynamics
• Consistency relations for large-scale structures: Applications for the integrated Sachs-Wolfe effect and the kinematic Sunyaev-Zeldovich effect
• A Consistency Relation for the CMB B-mode Polarization in the Squeezed Limit