Scale Transformations, Tree-level Perturbation Theory, and the Cosmological Matter Bispectrum

Abstract

Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths. Here we generalize this approach to investigate the usefulness of scale transformations for nonlinear higher-order statistics, specifically the bispectrum. We find that the bispectrum predicted by perturbation theory at tree-level can be rescaled to match the results of full numerical simulations in the weakly and intermediately nonlinear regimes, especially at high redshifts, with an accuracy that is surprising given the simplicity of the procedure used. This discovery not only offers a simple practical way of calculating the matter bispectrum, but also suggests that scale transformations may yet yield even deeper insights into the physics of hierarchical clustering.

6 pages, 3 figures; revised version accepted for publication in MNRAS

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• Combining perturbation theories with halo models for the matter bispectrum
• Large-scale structure perturbation theory without losing stream crossing
• The Matter Bispectrum in N-body Simulations with non-Gaussian Initial Conditions
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Modeling of weak lensing statistics. I. Power spectrum and bispectrum
• Modeling of weak lensing statistics. II. Configuration-space statistics
• A redshift distortion free correlation function at third order in the nonlinear regime
• About One-point Statistics of the Ratio of Two Fourier-transformed Cosmic Fields and an Application