• methods: N-body simulations;
  • cosmology: theory;
  • large-scale structure of Universe


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 decrease, and this evolution is not well accounted for by the previous scaling formulae. This breakdown of stable clustering can be understood as resulting from the modification of dark matter haloes by continuing mergers. These effects are naturally included in the analytic ‘halo model’ for non-linear structure; we use this approach to fit both our scale-free results and also our previous cold dark matter data. This method is more accurate than the commonly used Peacock–Dodds formula and should be applicable to more general power spectra. Code to evaluate non-linear power spectra using this method is available from Following publication, we will make the power-law simulation data publically available through the Virgo website