Nonlinear growth of structure in cosmologies with damped matter fluctuations

We investigate the nonlinear evolution of structure in variants of the standard cosmological model which display damped density fluctuations relative to cold dark matter (e.g. in which cold dark matter is replaced by warm or interacting DM). Using N-body simulations, we address the question of how much information is retained from different scales in the initial linear power spectrum following the nonlinear growth of structure. We run a suite of N-body simulations with different initial linear matter power spectra to show that, once the system undergoes nonlinear evolution, the shape of the linear power spectrum at high wavenumbers does not affect the non-linear power spectrum, while it still matters for the halo mass function. Indeed, we find that linear power spectra which differ from one another only at wavenumbers larger than their half-mode wavenumber give rise to (almost) identical nonlinear power spectra at late times, regardless of the fact that they originate from different models with damped fluctuations. On the other hand, the halo mass function is more sensitive to the form of the linear power spectrum. Exploiting this result, we propose a two parameter model of the transfer function in generic damped scenarios, and show that this parametrisation works as well as the standard three parameter models for the scales on which the linear spectrum is relevant.