[Paper Review] Full-shape analysis with simulation-based priors: cosmological parameters and the structure growth anomaly

Mikhail M. Ivanov, Andrej Obuljen+2 more|arXiv (Cornell University)|Sep 16, 2024

Astronomy and Astrophysical Research4 citations

TL;DR

This paper introduces a simulation-based prior framework for full-shape galaxy clustering analysis, combining effective field theory (EFT) on large scales with 10,500 HOD-based galaxy simulations to constrain EFT parameters. It achieves 30–60% improvements in constraints on Ωₘ and σ₈ (Ωₘ = 0.315 ± 0.010, σ₈ = 0.671 ± 0.027), reaffirming the structure growth tension in the ΛCDM model.

ABSTRACT

We explore full-shape analysis with simulation-based priors, which is the simplest approach to galaxy clustering data analysis that combines effective field theory (EFT) on large scales and numerical simulations on small scales. The core ingredient of our approach is the prior density of EFT parameters which we extract from a suite of 10500 galaxy simulations based on the halo occupation distribution (HOD) model. We measure the EFT parameters with the field-level forward model, which enables us to cancel cosmic variance. On the theory side, we develop a new efficient approach to calculate field-level transfer functions using time-sliced perturbation theory and the logarithmic fast Fourier transform. We find that the cosmology dependence of EFT parameters of galaxies is approximately degenerate with the HOD parameters, and hence it can be ignored for the purpose of prior generation. We use neural density estimation to model the measured distribution of EFT parameters. Our distribution model is then used as a prior in a reanalysis of the BOSS full-shape galaxy power spectrum data. Assuming the $Λ$CDM model, we find significant ($\approx 30\%$ and $\approx 60\%$) improvements for the matter density fraction and the mass fluctuation amplitude, which are constrained to $Ω_{m}= 0.315 \pm 0.010$ and $σ_8 = 0.671 \pm 0.027$. The value of the Hubble constant does not change, $H_0= 68.7\pm 1.1$~km/s/Mpc. This reaffirms earlier reports of the structure growth tension from the BOSS data. Finally, we use the measured EFT parameters to constrain the galaxy-dark matter connection.

Motivation & Objective

• To develop a robust, simulation-based prior for EFT parameters in galaxy clustering analysis, reducing reliance on ad hoc nuisance parameter marginalization.
• To improve cosmological constraints from BOSS full-shape data by incorporating realistic galaxy formation physics via HOD simulations.
• To test the cosmological independence of HOD-based EFT priors, ensuring prior robustness across different cosmological models.
• To validate the EFT framework for galaxy power spectra, including stochastic noise, up to k ≈ 0.45 h Mpc⁻¹ in redshift space.
• To quantify the impact of EFT parameter uncertainty on cosmological inference, particularly in the context of the structure growth tension.

Proposed method

• The authors generate a prior distribution of EFT parameters using 10,500 HOD-based galaxy simulations from the Abacus suite, capturing realistic galaxy clustering across diverse halo occupation models.
• They employ a field-level forward model to measure EFT parameters directly from simulations, enabling cosmic variance cancellation and accurate parameter inference.
• A new time-sliced perturbation theory approach with logarithmic fast Fourier transforms is developed to efficiently compute field-level transfer functions.
• Neural density estimation is used to model the measured EFT parameter distribution, which is then used as a prior in a reanalysis of BOSS full-shape data.
• The method combines EFT on large scales with simulation-based priors on small scales, avoiding the breakdown of perturbation theory in the non-linear regime.
• The cosmological dependence of EFT parameters is tested across three Abacus cosmologies (σ₈ = 0.75, 0.86, and fiducial), confirming that cosmology has a weaker effect than HOD variation on prior generation.

Figure 1: A typical HOD mock galaxy distribution in real space (upper panel) and redshift space (lower panel) from our set (left), field-level EFT fit to it (center), and the residuals (right). The overdensity field has been smoothed with a $R=4\,h^{-1}{\text{Mpc}}$ 3D Gaussian filter, the depth of

Experimental results

Research questions

• RQ1 Can simulation-based priors for EFT parameters significantly improve cosmological constraints in full-shape galaxy clustering analysis?
• RQ2 How does the inclusion of HOD-based simulations affect the precision of Ωₘ and σ₈ constraints compared to standard EFT approaches?
• RQ3 To what extent do EFT parameters depend on the underlying cosmology, and can this be safely ignored when generating priors?
• RQ4 Does the EFT framework accurately describe the stochastic noise power spectrum in redshift space up to k ≈ 0.45 h Mpc⁻¹?
• RQ5 What is the impact of EFT parameter uncertainty on the structure growth tension observed in BOSS data?

Key findings

• The method achieves a 30% improvement in the constraint on the matter density fraction, yielding Ωₘ = 0.315 ± 0.010.
• A 60% improvement is observed in the constraint on the mass fluctuation amplitude, resulting in σ₈ = 0.671 ± 0.027.
• The Hubble constant remains unchanged at H₀ = 68.7 ± 1.1 km/s/Mpc, consistent with prior BOSS analyses.
• The EFT model with higher-order corrections accurately predicts the noise power spectrum up to k ≈ 0.45 h Mpc⁻¹ in redshift space, with residuals scaling as k⁴.
• Cosmological dependence of EFT parameters is weaker than HOD variation, validating the use of a single prior across cosmologies.
• No evidence is found for a shallower noise power spectrum shape on quasi-linear scales, unlike in the dark matter case, suggesting EFT remains effective for galaxies with proper higher-order corrections.

Figure 2: Cosmological parameters from the EFT-based full shape analysis of the BOSS power spectrum with conservative and informative simulation-based priors on EFT parameters. For comparison, the Planck 2018 results for $\Lambda$ CDM+ $m_{\nu}$ are also shown.