High accuracy spectra at high z in dynamical dark energy simulations

Non-linear power spectra, at various redshift z, will be measured by the next generation mass probes, and this will allow to investigate the nature of DE. Seemingly, to exploit such data, we however need high precision spectral predictions, spanning the functional space of w(a) DE state equations, for the admitted cosmological parameter ranges. In this paper we show that data analysis can be simplified, by comparing them with w=const. models only, although allowing for different w's at different z. The point we test is that, at a any redshift z, spectra depend just on the r.m.s. fluctuation amplitude σ₈(z), the reduced density parameters ω_b,c and the distance d_LSB(z) from the Last Scattering Band. We test this through N-body simulations, by comparing dynamical DE models and auxiliary w=const. models. We find spectral discrepancies steadily <1%, but even smaller at higher redshift, where spectra approach a permil precision. An implicit conclusion, however, is that any w(z) law, deduced from data at various z, by testing them against constant-w models, is not the actual z-dependence of the DE state parameter.