Stable clustering, the halo model and non-linear cosmological power spectra

We present the results of a large library of cosmological N-body simulations, using power-law initial spectra. The non-linear evolution of the matter power spectra is compared with the predictions of existing analytic scaling formulae based on the work of Hamilton et al. The scaling approach has assumed that highly non-linear structures obey ‘stable clustering’ and are frozen in proper coordinates. Our results show that, when transformed under the self-similarity scaling, the scale-free spectra define a non-linear locus that is clearly shallower than would be required under stable clustering. Furthermore, the small-scale non-linear power increases as both the power spectrum index n and the density parameter Ω…