Exploring KSZ velocity reconstruction with $N$-body simulations and the halo model

TL;DR

This paper investigates the KSZ velocity reconstruction method using N-body simulations, revealing additional noise contributions and demonstrating its potential for cosmological studies with improved modeling.

Contribution

It introduces a refined noise model for KSZ velocity reconstruction based on a halo model and validates the method's unbiasedness in estimating primordial non-Gaussianity.

Findings

Reconstruction noise exceeds initial analytic predictions.

Additional noise terms from a six-point halo model explain discrepancies.

The method accurately recovers $f_{NL}$ with expected statistical errors.

Abstract

KSZ velocity reconstruction is a recently proposed method for mapping the largest-scale modes of the universe, by applying a quadratic estimator $\hat{v}_r$ to the small-scale CMB and a galaxy catalog. We implement kSZ velocity reconstruction in an $N$-body simulation pipeline and explore its properties. We find that the reconstruction noise can be larger than the analytic prediction which is usually assumed. We revisit the analytic prediction and find additional noise terms which explain the discrepancy. The new terms are obtained from a six-point halo model calculation, and are analogous to the $N^{(1)}$ and $N^{(3/2)}$ biases in CMB lensing. We implement an MCMC pipeline which estimates $f_{NL}$ from $N$-body kSZ simulations, and show that it recovers unbiased estimates of $f_{NL}$, with statistical errors consistent with a Fisher matrix forecast. Overall, these results confirm that kSZ velocity reconstruction will be a powerful probe of cosmology in the near future, but new terms should be included in the noise power spectrum.