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We study the matter bispectrum of the large-scale structure by comparingdifferent perturbative and phenomenological models with measurements from$N$-body simulations obtained with a modal bispectrum estimator. Using shapeand amplitude correlators, we directly compare simulated data with theoreticalmodels over the full three-dimensional domain of the bispectrum, for differentredshifts and scales. We review and investigate the main perturbative methodsin the literature that predict the one-loop bispectrum: standard perturbationtheory, effective field theory, resummed Lagrangian and renormalisedperturbation theory, calculating the latter also at two loops for some triangleconfigurations. We find that effective field theory (EFT) succeeds in extendingthe range of validity furthest into the mildly nonlinear regime, albeit at theprice of free extra parameters requiring calibration on simulations. For themore phenomenological halo model, we confirm that despite its validity in thedeeply nonlinear regime it has a deficit of power on intermediate scales, whichworsens at higher redshifts; this issue is ameliorated, but not solved, bycombined halo-perturbative models. We show from simulations that in thistransition region there is a strong squeezed bispectrum component that issignificantly underestimated in the halo model at earlier redshifts. We thuspropose a phenomenological method for alleviating this deficit, which wedevelop into a simple phenomenological "three-shape" benchmark model based onthe three fundamental shapes we have obtained from studying the halo model.When calibrated on the simulations, this three-shape benchmark model accuratelydescribes the bispectrum on all scales and redshifts considered, providing aprototype bispectrum HALOFIT-like methodology that could be used to describeand test parameter dependencies.

Matter bispectrum of large-scale structure: Three-dimensional comparison between theoretical models and numerical simulations