One simulation to fit them all - changing the background parameters of a cosmological N-body simulation

We demonstrate that the output of a cosmological N-body simulation can, to remarkable accuracy, be scaled to represent the growth of large-scale structure in a cosmology with parameters similar to but different from those originally assumed. Our algorithm involves three steps: a reassignment of length, mass and velocity units; a relabelling of the time axis and a rescaling of the amplitudes of individual large-scale fluctuation modes. We test it using two matched pairs of simulations. Within each pair, one simulation assumes parameters consistent with analyses of the first-year Wilkinson Microwave Anisotropy Probe (WMAP) data. The other has lower matter and baryon densities and a 15 per cent lower fluctuation amplitude, consistent with analyses of the three-year WMAP data. The pairs differ by a factor of a thousand in mass resolution, enabling performance tests on both linear and non-linear scales. Our scaling reproduces the mass power spectra of the target cosmology to better than 0.5 per cent on large scales (k < 0.1hMpc^-1) both in real and in redshift space. In particular, the baryonic acoustic oscillation features of the original cosmology are removed and are correctly replaced by those of the target cosmology. Errors are still below 3 per cent for k < 1hMpc^-1. Power spectra of the dark halo distribution are even more precisely reproduced, with errors below 1 per cent on all scales tested. A halo-by-halo comparison shows that centre-of-mass positions and velocities are reproduced to better than 90h^-1kpc and 5 per cent, respectively. Halo masses, concentrations and spins are also reproduced at about the 10 per cent level, although with small biases. Halo assembly histories are accurately reproduced, leading to central galaxy magnitudes with errors of about 0.25mag and a bias of about 0.13mag for a representative semi-analytic model. This algorithm will enable a systematic exploration of the coupling between cosmological parameter estimates and uncertainties in galaxy formation in future large-scale structure surveys.