Transverse velocities and matter gradient correlations: a new signal and a new challenge to moving-lens analyses

An observer that is moving towards a high-density region sees, on average, a higher matter density and more foreground-emitting sources ahead than behind themself. Consequently, the average abundance and luminosity of objects producing cosmological signals around an in-falling dark matter halo is larger in the direction of the halo's motion. In this Letter, we demonstrate this effect from simulated cosmological maps of the thermal Sunyaev Zel'dovich effect and the cosmic infrared background. We find that, for a wide range of halo masses and redshifts, oriented stacked profiles of these foregrounds show significant, potentially detectable gradients aligned with the transverse velocity of halos. The signal depends on the halo's mass and redshift, as well as the physical properties of the cosmic web surrounding the halos. We show that this signal is sufficiently prominent to be detected in future Cosmic Microwave Background experiments, therefore offering a new window into the study of cosmological structures. We argue that the dipolar morphological structure of this signal, its orientation, as well as its overall large amplitude, constitute a challenge for the detection of the transverse velocity through the study of the moving lens effect for stacked halos.