Beecroft Institute for Particle Astrophysics and Cosmology

The cross-correlation between weak lensing (WL) and the thermal Sunyaev-Zel'dovich (tSZ) effect probes the connection between the matter distribution and the thermal state of baryons at low redshift (z≲1). A key systematic in such measurements is contamination by extragalactic foregrounds, particularly the cosmic infrared background (CIB). Here we describe the CIB spectral energy distribution (SED) with a small number of physically motivated spectral parameters, calibrated against external measurements of the radiation field intensity in galaxies. Their uncertainty is then propagated into the recovered WL×tSZ signal in component separation at the level of the multi-frequency cross-power spectra rather than the map level. Applying this method to cosmic shear from the Dark Energy Survey and frequency maps from Planck, we show that the resulting measurements of the WL×tSZ power spectrum are insensitive to variations in the effective CIB spectral index, radio source contamination, and the scale and redshift dependence of the SED. The measurements are robust to realistic foreground uncertainties, supporting their use as probes of baryonic feedback and cosmology, and providing a framework for future high-precision surveys. We compare our measurements with the Flamingo suite of hydrodynamical simulations and find that they are compatible with the Flamingo predictions for a low amplitude of matter fluctuations, parametrised by S8, strongly disfavouring the larger S8 preferred by Planck. This result is independent of the impact of baryonic feedback as modelled in Flamingo.

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.