Amending the halo model to satisfy cosmological conservation laws
Alice Y. Chen, Niayesh Afshordi
Abstract
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 conservation, respectively. For example, the standard halo model overpredicts the 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 as the weak lensing power spectrum. Furthermore, we compare our results to previous work and argue that the amended halo model provides a more efficient and accurate framework to capture physical effects that happen in the process of cosmological structure formation.