Amending the halo model to satisfy cosmological conservation laws
  One of the most powerful tools in the arsenal of theoretical cosmologists is
the halo model of large scale structure, which provides a phenomenological
description of nonlinear structure in our universe. However, it is well known
that there is no simple way to impose conservation laws in the halo model. This
can severely impair the predictions on large scales for observables such as
weak lensing or the kinematic Sunyaev-Zel'dovich effect, which should satisfy
mass and momentum conservations, respectively. For example, the standard halo
model overpredicts weak lensing power spectrum by $> 8\%$ on scales $>20$
degrees. To address this problem, we present an $Amended ~ Halo ~ Model$,
explicitly separating the linear perturbations from $compensated$ halo
profiles. This is guaranteed to respect conservation laws, as well as linear
theory predictions on large scales. We then provide a simple fitting function
for the compensated halo profiles, and discuss the modified predictions for
1-halo and 2-halo terms, as well as other cosmological observations such weak
lensing power spectrum. Furthermore, we argue that the amended halo model
provides a more accurate framework to capture physical effects that happen in
the process of cosmological structure formation.
