[Paper Review] The reach of next-to-leading-order perturbation theory for the matter bispectrum

D. Alkhanishvili, C. Porciani+5 more|arXiv (Cornell University)|Jul 16, 2021

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy107 references27 citations

TL;DR

This study evaluates next-to-leading-order (NLO) perturbation theory models for the matter bispectrum using a large suite of N-body simulations at redshift z=1. It finds that effective field theory (EFT) models have the broadest reach (up to k ≈ 0.19 h Mpc⁻¹), outperforming standard and resummed perturbation theories, but their accuracy is highly sensitive to counterterm fitting procedures, especially in low-volume surveys where results vary significantly between realizations.

ABSTRACT

We provide a comparison between the matter bispectrum derived with different flavours of perturbation theory at next-to-leading order and measurements from an unprecedentedly large suite of $N$-body simulations. We use the $\chi^2$ goodness-of-fit test to determine the range of accuracy of the models as a function of the volume covered by subsets of the simulations. We find that models based on the effective-field-theory (EFT) approach have the largest reach, standard perturbation theory has the shortest, and `classical' resummed schemes lie in between. The gain from EFT, however, is less than in previous studies. We show that the estimated range of accuracy of the EFT predictions is heavily influenced by the procedure adopted to fit the amplitude of the counterterms. For the volumes probed by galaxy redshift surveys, our results indicate that it is advantageous to set three counterterms of the EFT bispectrum to zero and measure the fourth from the power spectrum. We also find that large fluctuations in the estimated reach occur between different realisations. We conclude that it is difficult to unequivocally define a range of accuracy for the models containing free parameters. Finally, we approximately account for systematic effects introduced by the $N$-body technique either in terms of a scale- and shape-dependent bias or by boosting the statistical error bars of the measurements (as routinely done in the literature). We find that the latter approach artificially inflates the reach of EFT models due to the presence of tunable parameters.

Motivation & Objective

• To assess the accuracy and range of validity (reach) of next-to-leading-order perturbation theory models for the matter bispectrum.
• To determine how the reach of these models depends on simulation volume and statistical uncertainty.
• To investigate the impact of systematic effects from N-body simulations on model fitting and reach estimation.
• To evaluate the role of counterterm fitting procedures in EFT models and their influence on the inferred range of accuracy.
• To compare the performance of EFT, standard perturbation theory (SPT), and resummed schemes (RegPT, RLPT) under realistic simulation conditions.

Proposed method

• Uses two large N-body simulation suites (Minerva and Eos) with high dynamic range to measure the matter bispectrum and power spectrum at z=1.
• Applies χ² goodness-of-fit tests to quantify model accuracy across different k-modes, defining the reach as the maximum k where χ²/dof ≤ 1.
• Sub-samples simulation volumes to study the dependence of reach on statistical uncertainty and volume size.
• Tests multiple perturbative models: standard SPT, RegPT, RLPT, and EFT with free counterterms.
• Implements two systematic error treatments: scale- and shape-dependent bias from mass resolution and quadrature-summed uncorrelated errors (as in prior literature).
• Fits EFT counterterms using power spectrum data and evaluates their impact on bispectrum fit quality across different fitting strategies (e.g., fixing some parameters).

Experimental results

Research questions

• RQ1 What is the range of scales over which NLO perturbation theory models accurately describe the matter bispectrum in N-body simulations?
• RQ2 How does the reach of EFT models depend on the fitting procedure for counterterms, especially when only a subset of parameters are free?
• RQ3 How do systematic effects from N-body simulations (e.g., mass resolution, discreteness) affect the inferred reach of perturbative models?
• RQ4 How does the simulation volume influence the statistical uncertainty and the resulting model reach, particularly for models with free parameters?
• RQ5 To what extent do artificially inflated error bars (as used in prior studies) bias the perceived performance of EFT models?

Key findings

• EFT models exhibit the broadest reach for the matter bispectrum, extending up to k ≈ 0.19 h Mpc⁻¹ when counterterms are fitted to power spectrum data.
• For a Euclid-like survey volume (Δz=0.2 at z=1), the median reach of IR-resummed EFT is 0.25 h Mpc⁻¹ for the power spectrum and 0.18 h Mpc⁻¹ for the bispectrum.
• The reach of EFT models is highly sensitive to the counterterm fitting strategy: setting three counterterms to zero and fitting only c₀ from the power spectrum yields the best reach for volumes < 100 h⁻³ Mpc³.
• For larger volumes, fitting all four EFT counterterms improves performance, but the scatter in reach across realizations remains large (e.g., 0.19–0.34 h Mpc⁻¹ for EFT power spectrum at 68% confidence).
• Artificially inflating error bars quadratically (as in prior studies) dramatically extends the apparent reach of EFT models—up to 0.40 h Mpc⁻¹ for the power spectrum—due to tunable counterterms, which may lead to overestimation of model accuracy.
• Systematic effects from finite mass resolution (scale- and shape-dependent bias) have a minor impact (<10% change) on reach estimates, but the inclusion of uncorrelated systematic errors leads to a significant artificial inflation of EFT’s reach.