The amplitude of mass fluctuations and mass density of the universe constrained by strong gravitational lensing

We investigate the linear amplitude of mass fluctuations in the universe, sigma(8), and the present mass density parameter of the Universe, Omega(m), from statistical strong gravitational lensing. We use the two population model of lens halos with fixed cooling mass scale M-c = 3 x 10(13)h(-1)M(circle dot) to match the observed lensing probabilities, and leave sigma(8) or Omega(m) as a free parameter to be constrained by the data. Another varying parameter, the equation of state of dark energy omega,and its typical values of -1, -2/3, -1/2 and -1/3 are investigated. We find that sigma(8) is degenerate with Omega(m) in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: sigma(8)Omega(m)(0.6) approximate to 0.33. However, both sigma(8) less than or equal to 0.7 and Omega(m) less than or equal to 0.2 can be safely ruled out, the best fit is when sigma(8) = 1.0, Omega(m) = 0.3 and omega = -1. This result is different from that obtained by Bahcall & Bode, who gave sigma(8) = 0.98 +/- 0.1 and Omega(m) = 0.17 +/- 0.05. For sigma(8) = 1.0, the higher value of Omega(m) = 0.35 requires omega = -2/3 and Omega(m) = 0.40 requires omega = -1/2.