Mapping the cosmic mass distribution with stacked weak gravitational
  lensing and Doppler lensing
  Dark matter halos represent the highest density peaks in the matter
distribution. Conversely, cosmic voids are under-dense patches of the universe.
Probing the mass distribution of the universe requires various approaches,
including weak gravitational lensing that subtly modifies the shape of distant
sources, and Doppler lensing that changes the apparent size and magnitude of
objects due to peculiar velocities. In this work, we adopt both gravitational
and Doppler lensing effects to study the underlying matter distribution in and
around cosmic voids/halos. We use the relativistic $N$-body code
\texttt{gevolution}, to generate the mass perturbations and develop a new
ray-tracing code that relies on the design of the ray bundle method. We
consider three categories of halo masses and void radii, and extract the
cosmological information by stacking weak-lensing and Doppler lensing signals
around voids/halos. The results of this paper show that the most optimal
strategy that combines both gravitational and Doppler lensing effects to map
the mass distribution should focus on the redshift range $z\approx 0.3-0.4$.
The recommendation of this paper is that future spectroscopic surveys should
focus on these redshifts and utilise the gravitational and Doppler lensing
techniques to extract information about underlying matter distribution across
the cosmic web, especially inside cosmic voids. This could provide a
complimentary cosmological analysis for ongoing or future low-redshift
spectroscopic surveys.
