[Paper Review] A multitracer analysis for the eBOSS galaxy sample based on the effective field theory of large-scale structure

Ruiyang Zhao, Xiaoyong Mu+9 more|arXiv (Cornell University)|Aug 11, 2023

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy123 references3 citations

TL;DR

This study presents a multi-tracer full-shape analysis of the eBOSS DR16 luminous red galaxy and emission line galaxy samples using the Effective Field Theory of Large-Scale Structure (EFTofLSS). By combining Jeffreys and Gaussian priors to mitigate volume effects and break degeneracies, it achieves a 27.3% tighter constraint on σ₈ compared to single-tracer analysis, yielding H₀ = 70.0 ± 2.3 km s⁻¹ Mpc⁻¹, Ωₘ = 0.317⁺⁰.⁰¹⁷₋₀.⁰²¹, σ₈ = 0.787⁺⁰.⁰⁵⁵₋₀.⁰⁶², and S₈ = 0.809⁺⁰.⁰⁶⁴₋₀.⁰⁷⁸, consistent with Planck 2018 results.

ABSTRACT

We perform a multitracer full-shape analysis in Fourier space based on the effective field theory of large-scale structure (EFTofLSS) using the complete Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 luminous red galaxy (LRG) and emission line galaxy (ELG) samples. We study in detail the impact of the volume projection effect and different prior choices when doing the full-shape analysis based on the EFTofLSS model. We show that adopting a combination of Jeffreys prior and Gaussian prior can mitigate the volume effect and avoid exploring unphysical regions in the parameter space at the same time, which is crucial when jointly analysing the eBOSS LRG and ELG samples. We validate our pipeline using 1000 eBOSS EZmocks. By performing a multitracer analysis on mocks with comparable footprints, we find that cosmological constraints can be improved by $\sim10-35$ per cent depending on whether we assume zero stochastic terms in the cross power spectrum, which breaks the degeneracy and boosts the constraints on the standard deviation of matter density fluctuation $σ_8$. Combining with the Big Bang Nucleosynthesis (BBN) prior and fixing the spectral tilt $n_s$ to Planck value, our multitracer full-shape analysis measures $H_0=70.0\pm2.3~{\mathrm{km}}~{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$, $Ω_m=0.317^{+0.017}_{-0.021}$, $σ_8=0.787_{-0.062}^{+0.055}$ and $S_8=0.809_{-0.078}^{+0.064}$, consistent with the Planck~2018 results. In particular, the constraint on $σ_8$ is improved beyond that obtained from the single tracer analysis by $18$ per cent, or by $27$ per cent when assuming zero stochastic terms in the cross power spectrum.

Motivation & Objective

• To improve cosmological constraints from the eBOSS DR16 galaxy sample by applying a multi-tracer full-shape analysis within the EFTofLSS framework.
• To investigate the impact of volume projection effects and prior choices on parameter inference in multi-tracer clustering analysis.
• To validate the analysis pipeline using 1000 eBOSS EZmocks and assess performance on realistic survey footprints.
• To quantify improvements in cosmological constraints from multi-tracer analysis, especially on σ₈, by breaking degeneracies with stochastic terms.
• To provide a robust, publicly available analysis pipeline for future surveys like DESI.

Proposed method

• The analysis uses the EFTofLSS model to describe the redshift-space power spectrum of LRG and ELG tracers, incorporating nonlinear corrections and stochasticity parameters.
• A combination of Jeffreys prior on the EFT counterterm and Gaussian prior on bias parameters is employed to suppress unphysical regions and mitigate volume effects.
• The full-shape likelihood is computed in Fourier space using k-modes up to k_max = 0.20 h Mpc⁻¹, with cosmic variance and shot noise properly modeled.
• Cosmological constraints are derived by marginalizing over all bias and stochasticity parameters, with the spectral index n_s fixed to the Planck 2018 value.
• The pipeline is validated on 1000 eBOSS EZmocks with comparable survey footprints to the real data.
• A DESI-like forecast is performed using mocks to project improvements for future surveys under similar conditions.

Figure 1: Footprint of LRG (red) and ELG (blue) samples in the North Galactic Cap (NGC) and South Galactic Cap (SGC) used in this analysis.

Experimental results

Research questions

• RQ1 How does the choice of prior—specifically Jeffreys versus Gaussian—impact the inference of cosmological parameters in multi-tracer EFTofLSS analysis?
• RQ2 To what extent does multi-tracer analysis reduce statistical uncertainties in σ₈, H₀, and S₈ compared to single-tracer analysis?
• RQ3 Can the volume projection effect be effectively mitigated through prior selection in full-shape EFTofLSS modeling?
• RQ4 How do assumptions about stochastic terms in the cross-power spectrum affect cosmological constraints?
• RQ5 What is the expected improvement in cosmological constraints from a DESI-like multi-tracer survey using the same EFTofLSS framework?

Key findings

• The combination of Jeffreys and Gaussian priors effectively mitigates the volume projection effect and avoids unphysical regions in parameter space during joint LRG and ELG analysis.
• The multi-tracer full-shape analysis improves the Figure of Merit by 62.7% compared to single LRG analysis, with σ₈ uncertainty reduced by 27.3% in the baseline analysis.
• Assuming zero stochastic terms in the cross-power spectrum boosts the improvement in σ₈ constraints to 40%, and to 30% for H₀ and Ωₘ in the DESI-like forecast.
• The final cosmological constraints are H₀ = 70.0 ± 2.3 km s⁻¹ Mpc⁻¹, Ωₘ = 0.317⁺⁰.⁰¹⁷₋₀.⁰²¹, σ₈ = 0.787⁺⁰.⁰⁵⁵₋₀.⁰⁶², and S₈ = 0.809⁺⁰.⁰⁶⁴₋₀.⁰⁷⁸, consistent with Planck 2018 results.
• The analysis shows that improvements stem from breaking degeneracies between stochasticity and cosmological parameters, not solely from cosmic variance cancellation.
• The method is validated on 1000 EZmocks and is publicly released via GitHub, enabling reproducibility and future application to DESI and other surveys.

Figure 2: Power spectrum multipoles measured from eBOSS DR16 LRG and ELG data. Shadowed bands indicate the $1\sigma$ regions evaluated from 1000 EZmocks. Solid lines denote the best-fit curves from our baseline analysis by performing a joint fit to all power spectrum measurements in both NGC and SGC