Characterising the matter bispectrum of large-scale structure: halo models, perturbation theory and a three-shape model

Andrei Lazanu, Tommaso Giannantonio, Marcel Schmittfull, E. P. S. Shellard

Published 2015-11-06Version 1

We study the matter bispectrum of large-scale structure by comparing the predictions of different perturbative and phenomenological models with the full three-dimensional bispectrum from $N$-body simulations estimated using modal methods. We show that among the perturbative approaches, effective field theory succeeds in extending the range of validity furthest on intermediate scales, at the cost of free additional parameters. By studying the halo model, we show that although it is satisfactory in the deeply non-linear regime, it predicts a deficit of power on intermediate scales, worsening at redshifts $z>0$. By comparison with the $N$-body bispectrum on those scales, we show that there is a significant squeezed component underestimated in the halo model. On the basis of 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; after calibration this fits the simulations on all scales and redshifts of interest. This method provides a prototype bispectrum \textsc{Halofit}-like methodology that could be used to describe and test parameter dependencies and should be relevant for the bispectrum of weak gravitational lensing and wider applications.