A test of the Suyama-Yamaguchi inequality from weak lensing

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 pieces of Bayesian evidence for a violation of the Suyama-Yamaguchi (SY) relation tau(NL) a parts per thousand yen (6f(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) a parts per thousand integral 10(2) and tau(NL) a parts per thousand integral 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.