  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 WMAP data. The other has
lower matter and baryon densities and a 15% 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 nonlinear scales. Our scaling reproduces the mass power spectra of
the target cosmology to better than 0.5% on large scales (k < 0.1 h/Mpc) both
in real and in redshift space. In particular, the BAO features of the original
cosmology are removed and are correctly replaced by those of the target
cosmology. Errors are still below 3% for k < 1 h/Mpc. Power spectra of the dark
halo distribution are even more precisely reproduced, with errors below 1% on
all scales tested. A halo-by-halo comparison shows that centre-of-mass
positions and velocities are reproduced to better than 90 kpc/h and 5%,
respectively. Halo masses, concentrations and spins are also reproduced at
about the 10% level, although with small biases. Halo assembly histories are
accurately reproduced, leading to central galaxy magnitudes with errors of
about 0.25 magnitudes and a bias of about 0.13 magnitudes for a representative
semi-analytic model.
