[Paper Review] {\sc SimBIG}: Cosmological Constraints using Simulation-Based Inference of Galaxy Clustering with Marked Power Spectra

Elena Massara, ChangHoon Hahn+8 more|arXiv (Cornell University)|Apr 5, 2024

Cosmology and Gravitation Theories4 citations

TL;DR

This paper introduces SimBIG, a simulation-based inference framework that uses marked power spectra to extract non-Gaussian cosmological information from galaxy clustering in the BOSS CMASS SGC survey. By applying normalizing flows to forward-model galaxy distributions from N-body simulations, it achieves 1.2× tighter constraints on σ₈ (0.777⁺⁰.⁰⁷⁷₋⁰.⁰⁷¹) than perturbation theory power spectrum analysis, demonstrating improved sensitivity to structure growth on nonlinear scales.

ABSTRACT

We present the first $Λ$CDM cosmological analysis performed on a galaxy survey using marked power spectra. The marked power spectrum is the two-point function of a marked field, where galaxies are weighted by a function that depends on their local density. The presence of the mark leads these statistics to contain higher-order information of the original galaxy field, making them a good candidate to exploit the non-Gaussian information of a galaxy catalog. In this work we make use of \simbig, a forward modeling framework for galaxy clustering analyses, and perform simulation-based inference using normalizing flows to infer the posterior distribution of the $Λ$CDM cosmological parameters. We consider different mark configurations (ways to weight the galaxy field) and deploy them in the \simbig~pipeline to analyze the corresponding marked power spectra measured from a subset of the BOSS galaxy sample. We analyze the redshift-space mark power spectra decomposed in $\ell = 0, 2, 4$ multipoles and include scales up to the non-linear regime. Among the various mark configurations considered, the ones that give the most stringent cosmological constraints produce posterior median and $68\%$ confidence limits on the growth of structure parameters equal to $Ω_m=0.273^{+0.040}_{-0.030}$ and $σ_8=0.777^{+0.077}_{-0.071}$. Compared to a perturbation theory analysis using the power spectrum of the same dataset, the \simbig~marked power spectra constraints on $σ_8$ are up to $1.2 imes$ tighter, while no improvement is seen for the other cosmological parameters.

Motivation & Objective

• To develop a cosmological inference framework that extracts non-Gaussian information from galaxy clustering beyond the two-point function.
• To test whether marked power spectra—weighted by local density—improve cosmological constraints on ΛCDM parameters compared to standard power spectrum analysis.
• To apply simulation-based inference with normalizing flows to model likelihoods without assuming Gaussianity, enabling analysis down to nonlinear scales.
• To evaluate the effectiveness of different mark configurations in enhancing constraints on σ₈ and Ωₘ in a low-density, high-bias galaxy sample.

Proposed method

• The SimBIG framework generates synthetic galaxy catalogs using N-body simulations and a halo occupation distribution (HOD) model, incorporating survey geometry, masks, and fiber collisions.
• Marked power spectra Mₗ(k) are computed by weighting galaxies with a function of local density, encoding higher-order statistics beyond the standard power spectrum.
• Normalizing flows are trained on simulated data to learn the joint posterior distribution of cosmological parameters, bypassing the need for a parametric likelihood model.
• The method performs simulation-based inference (SBI) using normalizing flows to map summary statistics (marked power spectra) to cosmological parameter posteriors.
• Multiple mark configurations are tested by varying parameters R, p, and δₛ to explore different weighting schemes of the galaxy field.
• Validation is performed using mock challenges with alternative forward models to ensure robustness and accuracy of the inferred posteriors.

Experimental results

Research questions

• RQ1 Can marked power spectra provide tighter cosmological constraints than the standard power spectrum in a ΛCDM analysis of galaxy clustering?
• RQ2 How does the performance of marked power spectra vary across different mark configurations in a low-density, high-bias galaxy sample?
• RQ3 To what extent does simulation-based inference with normalizing flows improve constraints on σ₈ and Ωₘ compared to perturbation theory with Gaussian likelihoods?
• RQ4 Does up-weighting low-density regions via marks enhance cosmological information extraction in the CMASS SGC sample?
• RQ5 Are marked power spectra effective for probing physics beyond ΛCDM, such as massive neutrinos or modified gravity, in future high-density surveys?

Key findings

• The best-performing mark configurations yield posterior constraints of Ωₘ = 0.273⁺⁰.⁰⁴⁰₋⁰.⁰³⁰ and σ₈ = 0.777⁺⁰.⁰⁷⁷₋⁰.⁰⁷¹ on the growth of structure parameters.
• The constraint on σ₈ is 1.2 times tighter than that obtained from a perturbation theory analysis of the same power spectrum data.
• No improvement is observed for Ωₘ, suggesting that marked power spectra do not enhance constraints on matter density in this sample.
• The improvement in σ₈ is consistent with that seen in prior SimBIG analyses using the power spectrum, indicating marked spectra do not add new information beyond what is already captured by the power spectrum in this context.
• The lack of improvement for Ωₘ and σ₈ suggests that low galaxy number density and high bias in the CMASS SGC sample limit the effectiveness of marks that emphasize low-density regions.
• Future SBI with denser, less biased samples—such as those from DESI, Euclid, or Roman—may unlock the full potential of marked power spectra for probing non-Gaussianity and physics beyond ΛCDM.