Tree-Level Bispectrum in the Effective Field Theory of Large-Scale Structure extended to Massive Neutrinos. (arXiv:1804.06849v2 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Belsunce_R/0/1/0/all/0/1">Roger de Belsunce</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Senatore_L/0/1/0/all/0/1">Leonardo Senatore</a>
We compute the tree-level bispectrum of dark matter in the presence of
massive neutrinos in the mildly non-linear regime in the context of the
effective field theory of large-scale structure (EFTofLSS). For neutrinos,
whose typical free streaming wavenumber ($k_{rm fs}$) is longer than the
non-linear scale ($k_{mathrm{NL}}$), we solve a Boltzmann equation coupled to
the effective fluid equation for dark matter. We solve perturbatively the
coupled system by expanding in powers of the neutrino density fraction
($f_{nu}$) and the ratio of the wavenumber of interest over the non-linear
scale ($k/k_{mathrm{NL}}$) and add suitable counterterms to remove the
dependence from short distance physics. For equilateral configurations, we find
that the total-matter tree-level bispectrum is approximately $16f_{nu}$ times
the dark matter one on short scales ($k > k_{rm fs}$). The largest
contribution stems from the back-reaction of massive neutrinos on the dark
matter growth factor. On large scales ($k < k_{rm fs}$) the contribution of
neutrinos to the bispectrum is smaller by up to two orders of magnitude.
We compute the tree-level bispectrum of dark matter in the presence of
massive neutrinos in the mildly non-linear regime in the context of the
effective field theory of large-scale structure (EFTofLSS). For neutrinos,
whose typical free streaming wavenumber ($k_{rm fs}$) is longer than the
non-linear scale ($k_{mathrm{NL}}$), we solve a Boltzmann equation coupled to
the effective fluid equation for dark matter. We solve perturbatively the
coupled system by expanding in powers of the neutrino density fraction
($f_{nu}$) and the ratio of the wavenumber of interest over the non-linear
scale ($k/k_{mathrm{NL}}$) and add suitable counterterms to remove the
dependence from short distance physics. For equilateral configurations, we find
that the total-matter tree-level bispectrum is approximately $16f_{nu}$ times
the dark matter one on short scales ($k > k_{rm fs}$). The largest
contribution stems from the back-reaction of massive neutrinos on the dark
matter growth factor. On large scales ($k < k_{rm fs}$) the contribution of
neutrinos to the bispectrum is smaller by up to two orders of magnitude.
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