[Paper Review] Higher-order statistics of the large-scale structure from photometric redshifts

Eleni Tsaprazi, Jens Jasche+2 more|arXiv (Cornell University)|Jan 9, 2023

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This paper presents a Bayesian framework that jointly infers 3D dark matter density, radial peculiar velocities, gravitational potential, and photometric redshift PDFs from galaxy clustering data, using Markov Chain Monte Carlo sampling. It achieves 86% cross-correlation with ground truth on 150 Mpc scales despite large redshift uncertainties (~300 Mpc), significantly improving structure reconstruction beyond 2-point statistics.

ABSTRACT

The large-scale structure is a major source of cosmological information. However, next-generation photometric galaxy surveys will only provide a distorted view of cosmic structures due to large redshift uncertainties. To address the need for accurate reconstructions of the large-scale structure in presence of photometric uncertainties, we present a framework that constrains the three-dimensional dark matter density jointly with galaxy photometric redshift probability density functions (PDFs), exploiting information from galaxy clustering. Our forward model provides Markov Chain Monte Carlo realizations of the primordial and present-day dark matter density, inferred jointly from data. Our method goes beyond 2-point statistics via field-level inference. It accounts for all observational uncertainties and the survey geometry. We showcase our method using mock catalogs that emulate next-generation surveys with a worst-case redshift uncertainty, equivalent to ${\sim}300$ Mpc. On scales $150$ Mpc, we improve the cross-correlation of the photometric galaxy positions with the ground truth from $28\%$ to $86\%$. The improvement is significant down to $13$ Mpc. On scales $150$ Mpc, we achieve a cross-correlation of $80-90\%$ with the ground truth for the dark matter density, radial peculiar velocities, tidal shear and gravitational potential.

Motivation & Objective

• To address the challenge of reconstructing the large-scale structure from photometric redshift surveys with large redshift uncertainties.
• To improve the accuracy of cosmic structure inference beyond 2-point statistics by leveraging field-level clustering information.
• To jointly constrain the 3D dark matter density field and individual photometric redshift probability density functions (PDFs).
• To enable accurate inference of cosmological fields such as peculiar velocities, tidal shear, and gravitational potential from low-accuracy photometric redshifts.
• To demonstrate the feasibility of extracting cosmological information at small scales even when redshift precision is limited.

Proposed method

• Uses a forward model that simulates galaxy counts based on Lagrangian Perturbation Theory (LPT) to evolve the initial dark matter density field to the present day.
• Employs a likelihood function that compares simulated galaxy counts to observed gridded data, incorporating survey geometry and masking.
• Applies Markov Chain Monte Carlo (MCMC) sampling to jointly infer the dark matter density field and photometric redshift PDFs from galaxy clustering.
• Incorporates a redshift-space distortion model that accounts for radial smearing due to photometric redshift errors.
• Uses the Simplex-In-Cell (SIC) estimator to reconstruct the peculiar velocity field at any point in space with high resolution.
• Solves Poisson’s equation in Fourier space to infer the gravitational potential and tidal shear from the dark matter density field.

Experimental results

Research questions

• RQ1 Can field-level inference from galaxy clustering improve the reconstruction of the large-scale structure when photometric redshift uncertainties are large?
• RQ2 To what extent can photometric redshift PDFs be constrained jointly with the dark matter density field?
• RQ3 Can peculiar velocities, gravitational potential, and tidal shear be accurately inferred from photometric data alone?
• RQ4 How well does the method recover cosmic structures on scales smaller than the redshift uncertainty?
• RQ5 What is the improvement in cross-correlation with ground truth when using joint inference versus standard photometric redshifts?

Key findings

• On scales of 150 Mpc, the cross-correlation between photometric galaxy positions and the ground truth increases from 28% to 86% after applying the method.
• The improvement in cross-correlation is significant down to 13 Mpc, demonstrating robustness at small scales.
• For the dark matter density field, the method achieves 80–90% cross-correlation with the ground truth on 150 Mpc scales.
• The method recovers radial peculiar velocities, tidal shear, and gravitational potential with 80–90% correlation to the ground truth on 150 Mpc scales.
• Despite a worst-case redshift uncertainty of ~300 Mpc, the method recovers individual cosmic filaments and structures in the dark matter distribution.
• The framework enables accurate inference of initial conditions of structure formation via the LPT-based evolution model.