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The Effective Halo Model: Creating a Physical and Accurate Model of the Matter Power Spectrum and Cluster Counts
Oliver H. E. Philcox, David N. Spergel, Francisco Villaescusa-Navarro
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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=0.02h Mpc⁻¹ to k=1h Mpc⁻¹. Our key ansatz is that the number density of halos depends on the non-linear 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 super-sample 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 non-linear scale. We provide a publicly released Python code.
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