The Intrinsic Matter Bispectrum in $\Lambda$CDM

Abstract

We present a fully relativistic calculation of the matter bispectrum at second order in cosmological perturbation theory assuming a Gaussian primordial curvature perturbation. For the first time we perform a full numerical integration of the bispectrum for both baryons and cold dark matter using the second-order Einstein-Boltzmann code, SONG. We review previous analytical results and provide an improved analytic approximation for the second-order kernel in Poisson gauge which incorporates Newtonian nonlinear evolution, relativistic initial conditions, the effect of radiation at early times and the cosmological constant at late times. Our improved kernel provides a percent level fit to the full numerical result at late times for most configurations, including both equilateral shapes and the squeezed limit. We show that baryon acoustic oscillations leave an imprint in the matter bispectrum, making a significant impact on squeezed shapes.

Accepted for publication in JCAP. 17 pages + appendices, 6 figures. Code available at GitHub: http://github.com/coccoinomane/song

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• The large-scale 3-point correlation function of the SDSS BOSS DR12 CMASS galaxies
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• Einstein's signature in cosmological large-scale structure
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• Cosmological $N$-body simulations including radiation perturbations
• The observed galaxy bispectrum from single-field inflation in the squeezed limit
• Cosmological perturbations for two cold fluids in $\Lambda$CDM
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Imprints of local lightcone projection effects on the galaxy bispectrum. II
• Growth of structure in interacting vacuum cosmologies
• Local primordial non-Gaussianity in the relativistic galaxy bispectrum
• Relativistic cosmological large scale structures at one-loop
• General relativistic effects in the galaxy bias at second order
• Dynamics of cosmological perturbations at first and second order
• Analytical growth functions for cosmic structures in a $\Lambda$CDM Universe
• Second order cosmological perturbations: simplified gauge change formulas
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• The galaxy bias at second order in general relativity with Non-Gaussian initial conditions
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• Second order cosmological perturbations: new conserved quantities and the general solution at super-horizon scale
• Relativistic second-order initial conditions for simulations of large-scale structure
• Relativistic matter bispectrum of cosmic structures on the light cone
• Multi-Scale Perturbation Theory II: Solutions and Leading-Order Bispectrum in the $\Lambda$CDM Universe
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• Multipoles of the galaxy bispectrum on a light cone: wide-separation and relativistic corrections