Non-linear structure formation in cosmologies with early dark energy

We argue that a few per cent of "Early Dark Energy" can be detected by the statistics of nonlinear structures. The presence of Dark Energy during linear structure formation is natural in models where the current low Dark-Energy density is related to the age of the Universe rather than a new fundamental small parameter. Generalisation of the spherical collapse model shows that the linear collapse parameter delta(c) is lowered. The corresponding relative enhancement of weak gravitational lensing on arc-minute scales lowers the value of sigma(8) inferred from a given lensing amplitude, as compared to Lambda CDM. In the presence of Early Dark Energy, structures grow slower, such that for a given s8, the number of galaxies and galaxy clusters is substantially increased at moderate and high redshift. For realistic models, the number of clusters detectable through their thermal Sunyaev-Zel'dovich effect at redshift unity and above, e. g. with the Planck satellite, can be an order of magnitude larger than for CDM.