High-precision spectra for dynamical Dark Energy cosmologies from constant-w models

Spanning the whole functional space of cosmologies with any admissible DE state equations w(a) seems a need, in view of forthcoming observations, namely those aiming to provide a tomography of cosmic shear. In this paper I show that this duty can be eased and that a suitable use of results for constant-w cosmologies can be sufficient. More in detail, I ``assign'' here six cosmologies, aiming to span the space of state equations w(a) = w_o + w_a(1-a), for w_o and w_a values consistent with WMAP5 and WMAP7 releases and run N-body simulations to work out their non-linear fluctuation spectra at various redshifts z. Such spectra are then compared with those of suitable auxiliary models, characterized by constant w. For each z a different auxiliary model is needed. Spectral discrepancies between the assigned and the auxiliary models, up to k ~ 2-3 h Mpc^{-1}, are shown to keep within 1%. Quite in general, discrepancies are smaller at greater z and exhibit a specific trend across the w_o and w_a plane. Besides of aiming at simplifying the evaluation of spectra for a wide range of models, this paper also outlines a specific danger for future studies of the DE state equation, as models fairly distant on the w_0 - w_a plane can be easily confused.