Decaying $Λ$ 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 $Λ\propto a^{-m}$, where $a$ is the scale factor and $m$ is a parameter ($0 \leq m < 3$). We show that for given low values of the present matter density parameter $Ω_{m0}$, there is a wide range of values for $m$ for which the lensing rate is significantly smaller than that in cosmological constant ($Λ$) models. We also show that models with low $Ω_{m0}$ and $m\stackrel{>}{\sim}2$ have high likelihood to reproduce the observed lens statistics in the HST snapshot survey.

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