Dynamical Dark Energy simulations: high accuracy Power Spectra at high   redshift
  Accurate predictions on non--linear power spectra, at various redshift z, will be a basic tool to interpret cosmological data from next generation mass probes, so obtaining key information on Dark Energy nature. This calls for high precision simulations, covering the whole functional space of w(z) state equations and taking also into account the admitted ranges of other cosmological parameters; surely a difficult task. A procedure was however suggested, able to match the spectra at z=0, up to k~3, hMpc^{-1}, in cosmologies with an (almost) arbitrary w(z), by making recourse to the results of N-body simulations with w = const. In this paper we extend such procedure to high redshift and test our approach through a series of N-body gravitational simulations of various models, including a model closely fitting WMAP5 and complementary data. Our approach detects w= const. models, whose spectra meet the requirement within 1% at z=0 and perform even better at higher redshift, where they are close to a permil precision. Available Halofit expressions, extended to (constant) w \neq -1 are unfortunately unsuitable to fit the spectra of the physical models considered here. Their extension to cover the desired range should be however feasible, and this will enable us to match spectra from any DE state equation. 
Luciano Casarini, Andrea V. Maccio', Silvio A. Bonometto