Dark energy and the evolution of spherical overdensities

We use the non-linear spherical model in cold dark matter (CDM) cosmologies with dark energy to investigate the effects of dark energy on the growth of structure and the formation of virialised structures. We consider dark energy models with a constant equation of state parameter w. For -1<w<-1/3, clusters form earlier and are more concentrated in quintessence than in LambdaCDM models, but they form later and are less concentrated than in the corresponding open model with the same matter density and no dark energy. We point out some confusion in the literature around the expression of the collapse factor (ratio of the radius of the sphere at virialisation to that at turn-around) derived from the virial theorem. We use the Sheth & Tormen extension of the Press-Schechter framework to calculate the evolution of the cluster abundance in different models and show the sensitivity of the cluster abundance to both the amplitude of the mass fluctuations, sigma8, and the sigma8-w normalisation, selected to match either the cosmic microwave background observations or the abundance of X-ray clusters.