[Paper Review] Velocity reconstruction with the cosmic microwave background and galaxy surveys

Juan Cayuso, R Bloch+3 more|arXiv (Cornell University)|Nov 22, 2021

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This paper develops a robust framework for reconstructing the large-scale peculiar velocity field using cross-correlations between cosmic microwave background (CMB) secondary anisotropies—specifically the kinetic Sunyaev-Zel'dovich (kSZ) and moving lens (ML) effects—and photometric galaxy redshift surveys. Using a refined quadratic estimator formalism and a novel simulation pipeline, it demonstrates that velocity reconstruction is feasible with near-term experiments, despite challenges from systematics, redshift errors, and non-Gaussianity.

ABSTRACT

The kinetic Sunyaev Zel'dovich (kSZ) and moving lens effects, secondary contributions to the cosmic microwave background (CMB), carry significant cosmological information due to their dependence on the large-scale peculiar velocity field. Previous work identified a promising means of extracting this cosmological information using a set of quadratic estimators for the radial and transverse components of the velocity field. These estimators are based on the statistically anisotropic components of the cross-correlation between the CMB and a tracer of large scale structure, such as a galaxy redshift survey. In this work, we assess the challenges to the program of velocity reconstruction posed by various foregrounds and systematics in the CMB and galaxy surveys, as well as biases in the quadratic estimators. To do so, we further develop the quadratic estimator formalism and implement a numerical code for computing properly correlated spectra for all the components of the CMB (primary/secondary blackbody components and foregrounds) and a photometric redshift survey, with associated redshift errors, to allow for accurate forecasting. We create a simulation framework for generating realizations of properly correlated CMB maps and redshift binned galaxy number counts, assuming the underlying fields are Gaussian, and use this to validate a velocity reconstruction pipeline and assess map-based systematics such as masking. We highlight the most significant challenges for velocity reconstruction, which include biases associated with: modelling errors, characterization of redshift errors, and coarse graining of cosmological fields on our past light cone. Despite these challenges, the outlook for velocity reconstruction is quite optimistic, and we use our reconstruction pipeline to confirm that these techniques will be feasible with near-term CMB experiments and photometric galaxy redshift surveys.

Motivation & Objective

• To develop a comprehensive framework for reconstructing the large-scale peculiar velocity field using CMB secondary anisotropies and galaxy surveys.
• To assess the impact of key systematics—foregrounds, redshift errors, masking, and coarse-graining—on velocity reconstruction accuracy.
• To validate a numerical pipeline for generating correlated CMB and galaxy number count maps under Gaussian field assumptions.
• To quantify biases in quadratic estimators arising from modeling errors and non-linearities in the velocity field.
• To establish a foundation for future cosmological constraints using velocity reconstruction as a probe of primordial non-Gaussianity, modified gravity, and early-Universe physics.

Proposed method

• Extends the quadratic estimator formalism to include both radial (kSZ) and transverse (ML) velocity components using statistically anisotropic cross-power spectra between CMB and galaxy tracers.
• Develops a numerical code, ReCCO, to compute properly correlated power spectra for primary CMB, secondary CMB (kSZ, ML), foregrounds, and photometric redshift surveys with redshift errors.
• Constructs a simulation framework generating Gaussian realizations of CMB maps and redshift-binned galaxy number counts on the light cone, incorporating beam and noise effects.
• Validates the reconstruction pipeline using simulated data, assessing map-based systematics such as sky masking and harmonic-space artifacts.
• Applies principal component analysis to the reconstruction to visualize signal-dominated modes across angular scales and redshifts.
• Evaluates the impact of non-Gaussianity via the $N^{(3/2)}$ bias, though not fully computed in the light-cone picture, and discusses its potential relevance for cosmological parameter constraints.

Experimental results

Research questions

• RQ1 How accurately can the radial and transverse peculiar velocity fields be reconstructed using cross-correlations between CMB secondaries and photometric galaxy surveys?
• RQ2 What are the dominant systematics affecting velocity reconstruction, and how do they impact estimator bias and signal-to-noise?
• RQ3 To what extent do redshift error characterization and coarse-graining of cosmological fields on the light cone degrade reconstruction fidelity?
• RQ4 Can the quadratic estimator formalism reliably recover velocity fields in the presence of realistic CMB and galaxy survey systematics?
• RQ5 What is the feasibility of velocity reconstruction with upcoming CMB and photometric redshift surveys, given current computational and modeling limitations?

Key findings

• The velocity reconstruction pipeline successfully recovers the true velocity field in simulations, demonstrating the feasibility of the method with near-term experiments.
• Principal component maps of the reconstruction are signal-dominated across a wide range of angular scales and exhibit a clear, interpretable redshift distribution.
• Masking and map-based systematics significantly degrade reconstruction quality, necessitating future development of map-space reconstruction techniques.
• Modeling errors, redshift error characterization, and coarse-graining on the light cone are identified as the most significant challenges to accurate velocity reconstruction.
• The $N^{(3/2)}$ bias from non-Gaussianity is expected to be non-negligible in principle, though its full impact in the light-cone context remains to be quantified.
• The ReCCO code, publicly released, provides a validated and extensible framework for future analysis of CMB-galaxy cross-correlations in velocity reconstruction.