Decaying Lambda cosmologies and statistical properties of gravitational lenses

In this paper we investigate the statistical properties of gravitational lenses for models in which a cosmological term decreases with time as Lambda proportional to a(-m), where a is the scale factor, and m is a parameter (0 less than or equal to m < 3). We show that for given low values of the present matter density parameter Omega(m0), there is a wide range of values for m for which the lensing rate is significantly smaller than that in cosmological constant (Lambda) models. We also show that models with low Omega(m0) and m greater than or similar to 1 have a high likelihood of reproducing the observed lens statistics in the Hubble Space Telescope Snapshot Survey (HSTSS).