Nonlinear evolution of cosmological power spectra

TL;DR

This study extends the HKLM scaling framework for nonlinear evolution of cosmological power spectra to low-density and Λ-dominated universes, incorporating spectra with steep negative indices via a spectrum-dependent correction. It uses AP3M N-body simulations to map the nonlinear to linear power via Δ^2_NL(k_NL) = f_NL[Δ^2_L(k_L)] with a scale relation k_L = [1+Δ^2_NL(k_NL)]^{-1/3} k_NL, and finds that cosmology influences the mapping primarily through the growth factor g(Ω). A 10-parameter fitting formula is derived to capture both power-law and CDM spectra across open and flat models, with rms accuracy ≈ 12–14% in f_NL, and a tangent-slope adjustment is shown to be essential for CDM small-scale power. The results provide a practical forward-modeling tool for nonlinear power spectra and improve interpretation of clustering data in the nonlinear regime.

Abstract

Hamilton et al. have suggested an invaluable scaling formula which describes how the power spectra of density fluctuations evolve into the nonlinear regime of hierarchical clustering. This paper presents an extension of their method to low-density universes and universes with nonzero cosmological constant. We pay particular attention to models with large negative spectral indices, and give a spectrum-dependent fitting formula which is of significantly improved accuracy by comparison with an earlier version of this work. The tendency of nonlinear effects to increase power on small scales is stronger for spectra with more negative spectral indices, and for lower densities. However, for low-density models with a cosmological constant, the nonlinear effects are less strong than for an open universe of the same $Ω$.