Measuring cosmic bulk flow with kinetic Sunyaev-Zel'dovich velocity reconstruction

Cosmic bulk flow–the volume-averaged peculiar velocity of matter–serves as a fundamental test of the Cosmological Principle when probed on gigaparsec (Gpc) scales. Historically, however, measurements of cosmic bulk flow have been limited to $R\lesssim 100h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$. We present an application of kinetic Sunyaev-Zel’dovich (kSZ) velocity reconstruction to constrain the bulk flow on cosmological scales, over a volume of effective radius $R\sim 2000h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$. We use the WISE$\times$SuperCOSMOS and unWISE galaxy catalogs, combined with CMB temperature maps from Planck to reconstruct large-scale velocities in six tomographic bins spanning $0.1\lesssim z\lesssim 1.5$. We place some of the tightest upper limits to date on bulk velocity at $200\lesssim R[h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}]\lesssim 2000$, finding results fully consistent with the $\mathrm{\Lambda }$CDM bulk flow expectation. Our unWISE constraints are in strong tension with the CatWISE quasar number-count dipole measurement if that dipole is due to a coherent bulk flow $\sim 370\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ at $R\sim 1000h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$. We also derive constraints on the matter power spectrum at low-$k$ ($k\lesssim {10}^{-3}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$) with low-$z$ ($z\sim 1$) galaxy samples. Alongside these cosmological constraints, we introduce a novel approach to map the optical depth bias–an inherent astrophysical degeneracy in kSZ velocity reconstruction–across different data combinations. Our work bridges the theoretical gap between bulk flow and kSZ-reconstructed velocities, and expands the horizon of bulk velocity measurements out to Gpc scales.