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

Abstract

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 http://as1.chem.nottingham.ac.uk/~res/software.html. Following publication, we will make the power‐law simulation data publically available through the Virgo website http://www.mpa-garching.mpg.de/Virgo/.

Constraining light gravitino mass from cosmic microwave background

“…In all cases we fixed the total dark matter density and energy density of gravitino as ω dm = 0.1099 and N 3/2 = 0.059, respectively. We adopt HALOFIT [30] in calculating nonlinear corrections.…”

“…[29]. For corrections for lensing potential due to nonlinear evolution of matter density perturbations, we adopt HALOFIT, which is based on the N-body simulations of CDM models [30]. Though the light gravitino model is not exactly the CDM models, we believe that the change of the nonlinear correction is negligible.…”

Simulations of Dark Energy Cosmologies

“…3.7. As this plot shows, the Smith et al (2003) expression accurately describes the evolution of the power spectrum at redshift 0 in both models and at earlier times. As the normalisation and linear spectral shape is the same in these two models, Halofit accurately reproduces the nonlinear power in each model at various redshifts once the appropriate linear growth factor for the dark energy model at that redshift is used.…”

“…The Zel'dovich approximation can induce small scale transients in the measured power spectrum. These transients die away after 10 expansion factors from the starting redshift (Smith et al, 2003). In order to limit the effects of the initial displacement scheme we chose a starting redshift of z = 200.…”

“…The AS model has a linear growth rate that differs from ΛCDM by ∼ 20% at z = 5. We also plot the Smith et al (2003) 'Halofit' empirical fitting function for ΛCDM and the AS model. The Halofit function has been incorporated into the CAMB package and this code was used to generate the output at various redshifts seen in Fig.…”