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We study the matter bispectrum of large-scale structure by comparing thepredictions of different perturbative and phenomenological models with the fullthree-dimensional bispectrum from $N$-body simulations estimated using modalmethods. We show that among the perturbative approaches, effective field theorysucceeds in extending the range of validity furthest on intermediate scales, atthe cost of free additional parameters. By studying the halo model, we showthat although it is satisfactory in the deeply non-linear regime, it predicts adeficit of power on intermediate scales, worsening at redshifts $z>0$. Bycomparison with the $N$-body bispectrum on those scales, we show that there isa significant squeezed component underestimated in the halo model. On the basisof these results, we propose a new three-shape model, based on the tree-level,squeezed and constant bispectrum shapes we identified in the halo model; aftercalibration this fits the simulations on all scales and redshifts of interest.We extend this model further to primordial non-Gaussianity of the local andequilateral types by showing that the same shapes can be used to describe theadditional non-Gaussian component in the matter bispectrum. This methodprovides a HALOFIT-like prototype of the bispectrum that could be used todescribe and test parameter dependencies and should be relevant for thebispectrum of weak gravitational lensing and wider applications.

physical review. d/physical review. d.

Matter bispectrum of large-scale structure with Gaussian and  non-Gaussian initial conditions: Halo models, perturbation theory, and a  three-shape model