The squeezed matter bispectrum covariance with responses

Abstract

We present a calculation of the angle-averaged squeezed matter bispectrum covariance Cov(Bm(k1, k1′, s1), Bm(k2, k2′, s2)), si ≪ ki,ki′ (i=1,2), that uses matter power spectrum responses to describe the coupling of large- to short-scale modes in the nonlinear regime. The covariance is given by a certain configuration of the 6-point function, which we show is dominated by response-type mode-coupling terms in the squeezed bispectrum limit. The terms that are not captured by responses are small, effectively rendering our calculation complete and predictive for linear s1,s2 values and any nonlinear values of k1,k1′,k2,k2′. Our numerical results show that the squeezed bispectrum super-sample covariance is only a negligible contribution. We also compute the power spectrum-bispectrum cross-covariance using responses. Our derivation for the squeezed matter bispectrum is the starting point to calculate analytical covariances for more realistic galaxy clustering and weak-lensing applications. It can also be used in cross-checks of numerical ensemble estimates of the general bispectrum covariance, given that it is effectively noise-free and complete in the squeezed limit.