Power spectrum for the small-scale Universe

Abstract

The first objects to arise in a cold dark matter 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=720^3 - 1584^3) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) propto k^n, with -2.5 < n < -1. Self-similar scaling is established for n=-1 and n=-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 quasilinear regime. In the nonlinear 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 vs. 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.Comment: 30 pages including 10 figures; accepted for publication in MNRA

Self-similar bumps and wiggles: Isolating the evolution of the BAO peak with power-law initial conditions

“…30,37] or in cCDM 2 sin(kr) goes as r 1 when k is small, and clearly varies rapidly with r when k is large. By contrast r −(n+2) varies as r −0.5 for n = −1.5 and r −1.5 for n = −0.5.…”

“…The latter constraint is more important, suggesting k max ≫ 2π/σ bao ≈ 13.3k bao . [37] choose k max ∼ k Ny = πN 1/3 /L box to make their PT predictions for powerlaw initial power spectra, but we feel that setting this upper limit according to the parameters of a simulation is a questionable thing to do when making ab initio predictions of non-linear behavior. Our PT predictions were calculated by modifying the publiclyavailable copter code from [20] to better accommodate powerlaw cosmologies and our setup.…”

“…In this paper, we pursue a complementary approach, inspired by N-body studies of self-similar cosmological models with a scale-free initial power spectrum P (k) = Ak n [e.g. [30][31][32][33][34][35][36][37]. Specifically, we investigate models in which the correlation function of the initial density field (the Fourier transform of its power spectrum) is ξ IC (r) = r 0 r at a "BAO" scale r bao .…”

Simulations of extragalactic magnetic fields and of their observables

“…Ryu et al, 2008), which in turn reflects the clustering of matter on these scales (e.g. Widrow et al, 2009). …”

Precision growth index using the clustering of cosmic structures and growth data

“…Finally, we would like to stress that we have taken into account the non-linear corrections by using the corresponding fitting formula introduced by [53], for the ΛCDM model (see also [54,55]). In their fitting formula there is one relatively free parameter, which is the slope of the power spectrum at the relevant scales, because the CDM power spectrum curves slowly and thus it varies as a function of scale according to: n eff = dlnP/dlnk.…”