A non-perturbative test of consistency relations and their violation
  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.
