The Gravitational Lensing Signatures of BOSS Voids in the Cosmic Microwave Background

We report a $5.3\sigma$ detection of the gravitational lensing effect of cosmic voids from the Baryon Oscillation Spectroscopic (BOSS) Data Release 12 seen in the $Planck$ 2018 cosmic microwave background (CMB) lensing convergence map. To make this detection, we introduce new optimal techniques for void stacking and filtering of the CMB maps, such as binning voids by a combination of their observed galaxy density and size to separate those with distinctive lensing signatures. We calibrate theoretical expectations for the void-lensing signal using mock catalogs generated in a suite of 108 full-sky lensing simulations from Takahashi et al. (2017). Relative to these templates, we measure the lensing amplitude parameter in the data to be $A_L=1.10 \pm 0.21$ using a matched-filter stacking technique, and confirm it using an alternative Wiener filtering method. We demonstrate that the result is robust against thermal Sunyaev-Zel'dovich contamination and other sources of systematics. We use the lensing measurements to test the relationship between the matter and galaxy distributions within voids, and show that the assumption of linear bias with a value consistent with galaxy clustering results is discrepant with observation at $\sim 3\sigma$; we explain why such a result is consistent with simulations and previous results, and is expected as a consequence of void selection effects. We forecast the potential for void-CMB lensing measurements in future data from the Advanced ACT, Simons Observatory and CMB-S4 experiments, showing that, for the same number of voids, the achievable precision improves by a factor of more than two compared to $Planck$.