A non-perturbative test of consistency relations and their violation

Abstract

In this paper, we verify the large scale structure consistency relations using N-body simulations, including modes in the highly non-linear regime. These relations (pointed out by Kehagias & Riotto and Peloso & Pietroni) follow from the symmetry of the dynamics under a shift of the Newtonian potential by a constant and a linear gradient, and predict the absence of certain poles in the ratio between the (equal time) squeezed bispectrum and power spectrum. The consistency relations, as symmetry statements, are exact, but have not been previously checked beyond the perturbative regime. Our test using N-body simulations not only offers a non-perturbative check, but also serves as a warm-up exercise for applications to observational data. A number of subtleties arise when taking the squeezed limit of the bispectrum--we show how to circumvent or address them. An interesting by-product of our investigation is an explicit demonstration that the linear-gradient symmetry is unaffected by the periodic boundary condition of the simulations. Lastly, we verify using simulations that the consistency relations are violated when the initial conditions are non-gaussian (of the local fNL type). The methodology developed here paves the way for constraining primordial non-gaussianity using large scale structure data, including (numerous) highly non-linear modes that are otherwise hard to interpret and utilize.

10 pages, 5 figures, 1 table

References in corpus (5)

• On the consistency relation of the 3-point function in single field inflation
• Conformal Symmetries of Adiabatic Modes in Cosmology
• Non-gaussianity and cosmic uncertainty in curvaton-type models
• Soft-Pion Theorems for Large Scale Structure
• Inflationary soft theorems revisited: A generalized consistency relation

Cited by in corpus (15)

• Primordial Non-Gaussianity from Biased Tracers: Likelihood Analysis of Real-Space Power Spectrum and Bispectrum
• Primordial non-Gaussianity from ultra slow-roll Galileon inflation
• The Covariance of Squeezed Bispectrum Configurations
• Consistency relations for large-scale structure in modified gravity and the matter bispectrum
• Large fluctuations and Primordial Black Holes
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Violation of the consistency relations for large-scale structure with dark energy
• Squeezing $f_{\mathrm{NL}}$ out of the matter bispectrum with consistency relations
• Soft theorems for boosts and other time symmetries
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Unifying attractor and non-attractor models of inflation under a single soft theorem
• Measuring Bias via the Consistency Relations of the Large Scale Structure
• First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies (An explanatory video is available at https://youtu.be/Zi36ooLPhss.)
• Model independent measurement of the growth rate from the consistency relations of the LSS
• Constraining $f_{NL}$ using the Large-Scale Modulation of Small-Scale Statistics