Abstract We investigate the linear amplitude of mass fluctuations in the universe, sigma8, and the present mass density parameter of the Universe, Ωm, from statistical strong gravitational lensing. We use the two population model of lens halos with fixed cooling mass scale Mc=3× 1013h-1M&sun; to match the observed lensing probabilities, and leave sigma8 or Ωm as a free parameter to be constrained by the data. Another varying parameter, the equation of state of dark energy ω, and its typical values of -1, -2/3, -1/2 and -1/3 are investigated. We find that sigma8 is degenerate with Ωm in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: sigma8Ωm^{0.6}≈ 0.33. However, both \sigma8≤ 0.7 and Ωm≤ 0.2 can be safely ruled out, the best fit is when sigma8=1.0, Ωm=0.3 and ω= -1. This result is different from that obtained by Bahcall & Bode, who gave sigma8 =0.98± 0.1 and Ωm =0.17± 0.05. For sigma8=1.0, the higher value of Ωm=0.35 requires ω =-2/3 and Ωm=0.40 requires ω=-1/2.

Keywords cosmology: theory --- cosmological parameters --- gravitational lensing

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