Power spectrum for the small-scale Universe

Lawrence M. Widrow, Pascal J. Elahi, Robert J. Thacker, Mark Richardson, Evan Scannapieco

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


The first objects to arise in a cold dark matter (CDM) universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N = 7203-15843) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) ∝ kn, with -2.5 ≤ n ≤ - 1. Self-similar scaling is established for n = -1 and -2 more convincingly than in previous, lower resolution simulations and for the first time, self-similar scaling is established for an n = -2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n = -2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasi-linear regime. In the non-linear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis versus halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.

Original languageEnglish (US)
Pages (from-to)1275-1285
Number of pages11
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
StatePublished - Aug 2009


  • Dark matter
  • Methods: N-body simulations

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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