The squeezed matter bispectrum covariance with responses. (arXiv:1901.01243v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Barreira_A/0/1/0/all/0/1">Alexandre Barreira</a>
We present a calculation of the angle-averaged squeezed matter bispectrum
covariance ${rm Cov}left(B_{m}(k_1, k_1′, s_1), B_{m}(k_2, k_2′,
s_2)right)$, $s_i ll k_i,k_i’$ ($i=1,2$), 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
$k_1,k_1′,k_2,k_2’$. 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.
We present a calculation of the angle-averaged squeezed matter bispectrum
covariance ${rm Cov}left(B_{m}(k_1, k_1′, s_1), B_{m}(k_2, k_2′,
s_2)right)$, $s_i ll k_i,k_i’$ ($i=1,2$), 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
$k_1,k_1′,k_2,k_2’$. 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.
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