The squeezed matter bispectrum covariance with responses

Abstract

We present a calculation of the angle-averaged squeezed matter bispectrum covariance $\mathrm{Cov}\left(B_m(k_1,k_1^{\prime },s_1),B_m(k_2,k_2^{\prime },s_2)\right)$, $s_i\ll k_i,k_i^{\prime }$ ($i=1,2$), 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 $s_1,s_2$ values and any nonlinear values of $k_1,k_1^{\prime },k_2,k_2^{\prime }$. 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.

29 pages + appendices; 3 figures and 1 table. The busy reader can focus on the summary in the Introduction, Table 1 and Section 6 with results. Comments welcomed. v2: minor corrections to the text; version published on JCAP

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