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.