Non-linear evolution of cosmological power spectra

Hamilton et al. have suggested an invaluable scaling formula which describes how the power spectra of density fluctuations evolve into the non-linear regime of hierarchical clustering. This paper presents an extension of their method to low-density universes and universes with non-zero cosmological constant. We pay particular attention to models with large negative spectral indices, and give a spectrum-dependent fitting formula which is of significantly improved accuracy by comparison with an earlier version of this work. The tendency of non-linear effects to increase power on small scales is stronger for spectra with more negative spectral indices, and for lower densities. However, for low-density models with a cosmological constant, the non-linear effects are less strong than for an open universe of the same Ω.