The 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 $k=0.02h\,\mathrm{Mpc}^{-1}$ to
$k=1h\,\mathrm{Mpc}^{-1}$. 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 ($\sim 10\%$) 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.
