Cosmology

We examine, from first principles, the angular power spectrum between the kinematic Sunyaev-Zel'dovich effect (kSZ) and the reconstructed galaxy momentum -- the basis of existing and future "kSZ stacking" analyses. We present a comprehensive evaluation of all terms contributing to this cross-correlation, including both the transverse and longitudinal modes of the density-weighted velocity field, as well as all irreducible correlators that contribute to the momentum power spectrum. This includes the dominant component, involving the convolution of the electron-galaxy and velocity-velocity power spectra, an additional disconnected cross-term, and a connected non-Gaussian trispectrum term. Using this framework, we examine the impact of other commonly neglected contributions, such as the two-halo component of the dominant term, and the impact of satellite galaxies. Finally, we assess the sensitivity of upcoming CMB experiments to these effects and determine that they will be sensitive to the cross-term, the connected non-Gaussian trispectrum term, the two-halo contribution and impact of satellite galaxies, at a significance level of ~4-6 σ. On the other hand, the contribution from longitudinal modes is negligible in all cases. These results identify the astrophysical observables that must be accurately modelled to obtain unbiased constraints on cosmology and astrophysics from near-future kSZ measurements.

The moving lens (ML) effect is a secondary anisotropy of the cosmic microwave background (CMB) generated by the transverse motion of gravitational potentials, providing a direct probe of the large-scale cosmic velocity field. Its detection relies on cross-correlating a CMB map with the transverse galaxy momentum field, constructed from the galaxy overdensity and a velocity field reconstructed from it. Restricting the reconstruction to large-scale modes strongly suppresses contamination from small-scale astrophysical foregrounds while preserving the ML signal. In this work, we develop a theoretical framework for the ML estimator and its foreground contamination. We show that the signal and foregrounds have a distinct dependence on the direction of the long-wavelength mode represented by the reconstructed galaxy velocity. In the squeezed limit enforced by the velocity reconstruction filter, the bispectrum sourcing the foreground correlation becomes independent of this direction, causing its leading contribution to vanish after angular averaging. In turn, the ML signal survives by matching this directional dependence, with its amplitude reduced only by the filtered velocity variance. Using the halo model, we derive the leading corrections beyond the squeezed limit and show that the residual contamination remains parametrically suppressed. Finally, we model the cross-correlation exactly in the curved sky, and show that it is sourced solely by the longitudinal component of the galaxy momentum field, in the form of a spin-1 E-mode, with all other contributions either strongly suppressed on small scales or exactly zero.