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, σ8, and the present mass density parameter of the Universe, Ωm, from the statistical strong gravitational lensing. We use the two populations of lens halos model with fixed cooling mass scale Mc = 3× 10 hM⊙ to match the observed lensing probabilities, and leave σ8 or Ωm as a free parameter to be constrained by data. Another varying parameter is 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 σ8 is degenerate with Ωm in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: σ8Ω 0.6 m ≈ 0.33 (Bahcall & Bode 2003 and references therein). However, both σ8 ≤ 0.7 and Ωm ≤ 0.2 can be safely ruled out, the best value is when σ8 = 1.0, Ωm = 0.3 and ω = −1. This result is different from that obtained by Bahcall & Bode (2003), who gives σ8 = 0.98 ± 0.1 and Ωm = 0.17 ± 0.05. For σ8 = 1.0, higher value of Ωm = 0.35 requires ω = −2/3 and Ωm = 0.40 requires ω = −1/2.