A test of the Suyama-Yamaguchi inequality from weak lensing

TL;DR

This paper explores the potential of weak lensing surveys, specifically EUCLID, to test primordial non-Gaussianities and the Suyama-Yamaguchi inequality by analyzing convergence spectra, bispectra, and trispectra.

Contribution

It introduces a method to constrain non-Gaussianity parameters and assess the Suyama-Yamaguchi relation using weak lensing data and Monte Carlo techniques.

Findings

The Suyama-Yamaguchi relation can be tested down to f_nl~100 and tau_nl~10^5.

Analytical expressions for the probability of the relation being exactly fulfilled are derived.

The study demonstrates the feasibility of probing primordial non-Gaussianities with upcoming lensing surveys.

Abstract

We investigate the weak lensing signature of primordial non-Gaussianities of the local type by constraining the magnitude of the weak convergence bi- and trispectra expected for the EUCLID weak lensing survey. Starting from expressions for the weak convergence spectra, bispectra and trispectra, whose relative magnitudes we investigate as a function of scale, we compute their respective signal to noise ratios by relating the polyspectra's amplitude to their Gaussian covariance using a Monte-Carlo technique for carrying out the configuration space integrations. In computing the Fisher-matrix on the non-Gaussianity parameters f_nl, g_nl and tau_nl with a very similar technique, we can derive Bayesian evidences for a violation of the Suyama-Yamaguchi relation tau_nl>=(6 f_nl/5)^2 as a function of the true f_nl and tau_nl-values and show that the relation can be probed down to levels of f_nl~10^2 and tau_nl~10^5. In a related study, we derive analytical expressions for the probability density that the SY-relation is exactly fulfilled, as required by models in which any one field generates the perturbations. We conclude with an outlook on the levels of non-Gaussianity that can be probed with tomographic lensing surveys.