| Summary: | We address the degree and rapidity of generation of small-scale power over the course of structure formation in cosmologies where the primordial power spectrum is strongly suppressed beyond a given wavenumber. We first summarize the situations where one expects such suppressed power spectra and point out their diversity. We then employ an exponential cut-off, which characterizes warm dark matter (WDM) models, as a template for the shape of the cut-off and focus on damping scales ranging from 10 6 to 10 9 h -1 M ⊙. Using high-resolution simulations, we show that the suppressed part of the power spectrum is quickly (re)generated and catches up with both the linear and the non-linear evolution of the unsuppressed power spectrum. From z = 2 onwards, a power spectrum with a primordial cut-off at 10 9 h -1 MŁódź, becomes virtually indistinguishable from an evolved cold dark matter (CDM) power spectrum. An attractor such as that described in Zaldarriaga, Scoccimarro and Hui for power spectra with different spectral indices also emerges in the case of truncated power spectra. Measurements of z ∼ 0 non-linear power spectra at ∼100 h -1 kpc cannot rule out the possibility of linear power spectra damped below ∼10 9 h -1 M ⊙. Therefore, WDM or scenarios with similar features should be difficult to exclude in this way. © 2005 RAS.
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