[Paper Review] Cosmology with the Redshift-Space Galaxy Bispectrum Monopole at One-Loop Order

Oliver H. E. Philcox, Mikhail M. Ivanov+4 more|arXiv (Cornell University)|Jun 6, 2022

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy142 references80 citations

TL;DR

This paper develops a complete one-loop perturbation theory model for the redshift-space galaxy bispectrum monopole, incorporating nonlinear galaxy bias, infrared resummation, stochasticity, counterterms, and survey effects. Validated with high-precision N-body simulations, it shows that one-loop corrections significantly improve constraints on galaxy bias parameters and may enhance primordial non-Gaussianity constraints by ~30%, though marginalization over nuisance parameters limits gains in σ₈ precision.

ABSTRACT

We study the cosmological information content of the redshift-space galaxy bispectrum monopole at one-loop order in perturbation theory. We incorporate all effects necessary for comparison to data: fourth-order galaxy bias, infrared resummation (accounting for the non-linear evolution of baryon acoustic oscillations), ultraviolet counterterms, non-linear redshift-space distortions, stochastic contributions, projection, and binning effects. The model is implemented using FFTLog, and validated with the PT Challenge suite of $N$-body simulations, whose large volume allows for high-precision tests. Focusing on the mass fluctuation amplitude, $\sigma_8$, and galaxy bias parameters, we find that including one-loop corrections allow us to significantly extend the range of scales over which the bispectrum can be modeled, and greatly tightens constraints on bias parameters. However, this does not lead to noticeable improvements in the $\sigma_8$ errorbar due to the necessary marginalization over a large number of nuisance parameters with conservative priors. Analyzing a BOSS-volume likelihood, we find that the addition of the one-loop bispectrum may lead to improvements on primordial non-Gaussianity constraints by $\lesssim 30\%$ and on $\sigma_8$ by $\approx 10\%$, though we caution that this requires pushing the analysis to short scales where the galaxy bias parameters may not be correctly recovered; this may lead to biases in the recovered parameter values. We conclude that restrictive priors from simulations or higher-order statistics such as the bispectrum multipoles will be needed in order to realize the full information content of the galaxy bispectrum.

Motivation & Objective

• To develop a theoretically complete and numerically robust model for the one-loop redshift-space galaxy bispectrum monopole, including all relevant physical effects for comparison with real data.
• To validate the model against the PT Challenge N-body simulations, ensuring accuracy across a wide dynamic range of scales.
• To assess the cosmological information content of the one-loop bispectrum, particularly for constraining σ₈ and primordial non-Gaussianity.
• To investigate the impact of nuisance parameters—especially bias and stochasticity—on parameter inference and the potential for bias in recovered values at small scales.
• To evaluate the utility of the one-loop bispectrum for current and future large-scale structure surveys, such as BOSS, under realistic observational conditions.

Proposed method

• Constructs a one-loop galaxy bispectrum model using the Effective Field Theory of Large Scale Structure (EFTofLSS), including all relevant deterministic, counterterm, and stochastic contributions.
• Incorporates fourth-order galaxy bias operators, non-linear redshift-space distortions, and coordinate rescalings to model galaxy clustering in redshift space.
• Applies infrared resummation to account for non-linear evolution of baryon acoustic oscillations and ensures convergence of the perturbative series via proper counterterm treatment.
• Uses the FFTLog algorithm for efficient and accurate computation of loop integrals in configuration and momentum space.
• Implements bin-averaging and projection effects to match observational survey geometry and data reduction pipelines.
• Validates the model against the PT Challenge simulations, using mock data to test parameter recovery and assess systematic biases.

Experimental results

Research questions

• RQ1 How does the inclusion of one-loop corrections improve the modeling of the redshift-space galaxy bispectrum monopole compared to tree-level approximations?
• RQ2 To what extent do one-loop corrections tighten constraints on galaxy bias parameters and σ₈ in a likelihood analysis?
• RQ3 What is the impact of marginalizing over a large number of nuisance parameters on the error budget for σ₈ and primordial non-Gaussianity?
• RQ4 Can the one-loop bispectrum model provide measurable improvements in constraints on primordial non-Gaussianity in a BOSS-like survey?
• RQ5 What are the dominant sources of bias in parameter inference when pushing to small scales, and how can they be mitigated?

Key findings

• One-loop corrections significantly extend the range of scales over which the galaxy bispectrum can be modeled, enabling use of smaller-scale information.
• The inclusion of one-loop terms leads to a substantial tightening of constraints on galaxy bias parameters, particularly b₂, bG₂, and bΓ₃.
• Despite improved bias constraints, the error bar on σ₈ does not improve noticeably due to marginalization over a large number of nuisance parameters with conservative priors.
• For a BOSS-like survey, the one-loop bispectrum may improve constraints on primordial non-Gaussianity by up to ≲30% and on σ₈ by ≈10%, though this is contingent on pushing to small scales where bias parameters may not be accurately recovered.
• Prior volume effects—arising from limited data volume and marginalization—can induce shifts of up to 1.5σ in parameter posteriors, particularly at kB_max = 0.12 h Mpc⁻¹, suggesting systematic biases if not corrected.
• The study concludes that restrictive priors from simulations or higher-order statistics (e.g., bispectrum multipoles) are essential to fully unlock the information content of the galaxy bispectrum.