Nonperturbative 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-gradientsymmetry 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 nongaussian (of the local f NL 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.1 The split into two separate symmetries here follows the discussion of [17].

Measuring bias via the consistency relations of the large scale structure

“…where µ ≡ k • q, and we have omitted the time dependence. Notice that, as expected, and verified recently in N-body siumulations [6], the equal-time CR's contains no 1/q pole. The CR's imply a non-renormalization theorem for the µ 2 /b α (q), coefficient, which we are going to check in the next sections.…”

Violation of the consistency relations for large-scale structure with dark energy

“…Complementing precision perturbation theory for LSS, we have another important tool for understanding cosmological perturbations, namely the consistency relations for LSS in ΛCDM [20][21][22], which relate soft (i.e. small momenta) limits of (n + 1)-point correlation functions to nor lower-point correlation functions (see [23] for an extension to multiple soft limits and redshift space, and [24] for a verification of the consistency relations in N -body simulations). This kind of consistency relation was first pointed out in the context of single-field inflation [25].…”

The Covariance of Squeezed Bispectrum Configurations

“…It provides a much better approximation to the full covariance that can find application to likelihood and Fisher analyses (e.g. [28,32,52,54]) or to tests of consistency relations [64,[74][75][76]. These results could be affected by additional non-Gaussian contributions to the covariance, although in the realistic setting of an actual redshift survey the difference might be less relevant than in our ideal case (e.g.…”

“…Furthermore, we can use this covariance to assess the power of very squeezed configurations to constrain f loc NL , see e.g. [64,74].…”

“…This is much better than the Gaussian approximation that has an error ∼ 100% for squeezed configurations, and completely misses off-diagonal correlations. This has an important impact on observables that are particularly sensitive to squeezed configurations, such as primordial non-Gaussianity, 2 and in general for methods exploiting consistency relations in large scale structures [74][75][76]. Given that there are a large number of triangles in the mildly squeezed regime we consider, our findings are potentially relevant for constraints on any cosmological parameter.…”