Effective halo model: Creating a physical and accurate model of the matter power spectrum and cluster counts

We introduce a physically motivated model of the matter power spectrum, based on the halo model and perturbation theory. This model achieves 1% accuracy on all k -scales between k =0.02 h Mpc^-1 to k =1 h Mpc^-1 . Our key ansatz is that the number density of halos depends on the nonlinear density contrast filtered on some unknown scale R . Using the effective field theory of large scale structure to evaluate the two-halo term, we obtain a model for the power spectrum with only two fitting parameters: R and the effective "sound speed," which encapsulates small-scale physics. This is tested with two suites of cosmological simulations across a broad range of cosmologies and found to be highly accurate. Due to its physical motivation, the statistics can be easily extended beyond the power spectrum; we additionally derive the one-loop covariance matrices of cluster counts and their combination with the matter power spectrum. This yields a significantly better fit to simulations than previous models, and includes a new model for supersample effects, which is rigorously tested with separate universe simulations. At low redshift, we find a significant (∼10 %) exclusion covariance from accounting for the finite size of halos which has not previously been modeled. Such power spectrum and covariance models will enable joint analysis of upcoming large-scale structure surveys, gravitational lensing surveys, and cosmic microwave background maps on scales down to the nonlinear scale. We provide a publicly released Python code.