Power spectra to 1 per cent accuracy between dynamical dark energy cosmologies

For dynamical dark energy cosmologies we carry out a series of N-body gravitational simulations, achieving per cent level accuracy in the relative mass power spectra within 0. 1 < k < 3 at any redshift for values of the dark energy equation of state consistent with current observations. Such accuracy in the power spectrum is necessary for next generation cosmological mass probes. Our matching procedure reproduces the cosmic microwave background distance to last scattering and delivers sub-per cent level accuracy in the matter power spectra at z = 0 and approximate to 3. We discuss the physical implications for probing dark energy with surveys of large-scale structure.