Towards a self-consistent halo model for the nonlinear large-scale structure

The halo model is a theoretically and empirically well-motivated framework for predicting the statistics of the nonlinear matter distribution in the Universe. However, current incarnations of the halo model suffer from two major deficiencies: (i) they do not enforce the stress-energy conservation of matter; (ii) they are not guaranteed to recover exact perturbation theory results on large scales. Here, we provide a formulation of the halo model (EHM) that remedies both drawbacks in a consistent way, while attempting to maintain the predictivity of the approach. In the formulation presented here, mass and momentum conservation are guaranteed on large scales, and results of the perturbation theory and the effective field theory can, in principle, be matched to any desired order on large scales. We find that a key ingredient in the halo model power spectrum is the halo stochasticity covariance, which has been studied to a much lesser extent than other ingredients such as mass function, bias, and profiles of halos. As written here, this approach still does not describe the transition regime between perturbation theory and halo scales realistically, which is left as an open problem. We also show explicitly that, when implemented consistently, halo model predictions do not depend on any properties of low-mass halos that are smaller than the scales of interest.