Ringing the universe with cosmic emptiness: void properties through a
  combined analysis of stacked weak gravitational and Doppler lensing
  An essential aspect of cosmic voids is that these underdense regions provide
complementary information about the properties of our Universe. Unlike dense
regions, voids are avoided by matter and are less contaminated by baryonic
processes. The first step to understanding the properties of cosmic voids is to
correctly infer their mass profiles. In the literature, various techniques have
been implemented. In this paper, we review them and implement a new technique
that is based on Doppler lensing. We use a relativistic $N$-body code,
\textsc{Gevolution}, to generate cosmological mass perturbations and implement
a three-dimensional ray-tracing technique, which follows the evolution of a
ray-bundles. We focus on the various properties of cosmic voids (e.g. void size
function, 2-point correlation function, and the density profile of voids), and
compare the results with their universal trends. We show that when weak-lensing
is combined with the Doppler lensing we obtain even tighter constraints than
weak-lensing alone. We also obtain better agreement between density profiles
within central parts of voids inferred from lensing and density profiles
inferred from halo tracers. The implication of the result relevant to the
ongoing and prospective low-redshift spectroscopic surveys is briefly
discussed.
