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Cluster abundance measurements are among the most sensitive probes of theamplitude of matter fluctuations in the universe, which in turn can helpconstrain other cosmological parameters, like the dark energy equation of stateor neutrino mass. However, difficulties in calibrating the relation between thecluster observable and halo mass, and the lack of completeness information,make this technique particularly susceptible to systematic errors. Here weargue that a cluster abundance analysis using statistical weak lensing on thestacked clusters leads to a robust lower limit on the amplitude offluctuations. The method compares the average weak lensing signal measuredaround the whole cluster sample to a theoretical prediction, assuming that theclusters occupy the centers of all of the most massive halos above some minimummass threshold. If the amplitude of fluctuations is below a certain limitingvalue, there are too few massive clusters in this model and the theoreticalprediction falls below the observations. Since any effects that modify themodel assumptions can only decrease the theoretical prediction, the limitingamplitude becomes a robust lower limit. Here, we apply it to a volume limitedsample of 16,000 group/cluster candidates identified from isolated luminous redgalaxies (LRGs) in the Sloan Digital Sky Survey (SDSS). We find $\sigma_8(\Omega_m/0.25)^{0.5}>0.62$ at the 95% c.l. after taking into accountobservational errors in the lensing analysis. While this is a relatively weakconstraint, both the scatter in the LRG luminosity-halo mass relation and thelensing errors are large; the constraints could improve considerably in thefuture with more sophisticated cluster identification algorithms and smallererrors in the lensing analysis. [Abridged]Comment: 10 pages, 5 figures; new version has only very minor revisions to  match published versio

A robust lower limit on the amplitude of matter fluctuations in the universe from cluster abundance and weak lensing