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The redshift distribution of galactic-scale lensing systems provides alaboratory to probe the velocity dispersion function (VDF) of early-typegalaxies (ETGs) and measure the evolution of early-type galaxies at redshift z~ 1. Through the statistical analysis of the currently largest sample ofearly-type galaxy gravitational lenses, we conclude that the VDF inferredsolely from strong lensing systems is well consistent with the measurements ofSDSS DR5 data in the local universe. In particular, our results stronglyindicate a decline in the number density of lenses by a factor of two and a 20%increase in the characteristic velocity dispersion for the early-type galaxypopulation at z ~ 1. Such VDF evolution is in perfect agreement with the$\Lambda$CDM paradigm (i.e., the hierarchical build-up of mass structures overcosmic time) and different from "stellar mass-downsizing" evolutions obtainedby many galaxy surveys. Meanwhile, we also quantitatively discuss the evolutionof the VDF shape in a more complex evolution model, which reveals its strongcorrelation with that of the number density and velocity dispersion ofearly-type galaxies. Finally, we evaluate if future missions such as LSST canbe sensitive enough to place the most stringent constraints on the redshiftevolution of early-type galaxies, based on the redshift distribution ofavailable gravitational lenses.

The velocity dispersion function of early-type galaxies and its redshift evolution: the newest results from lens redshift test