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

Abstract

We investigate the linear amplitude of mass fluctuations in the universe, $σ_8$, and the present mass density parameter of the Universe, $Ω_\mathrm{m}$, from the statistical strong gravitational lensing. We use the two populations of lens halos model with fixed cooling mass scale $M_\mathrm{c}=3\times 10^{13}h^{-1}M_{\sun}$ to match the observed lensing probabilities, and leave $σ_8$ or $Ω_\mathrm{m}$ 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 $σ_8$ is degenerate with $Ω_\mathrm{m}$ in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: $σ_8Ω_\mathrm{m}^{0.6}\approx 0.33$ (Bahcall & Bode\cite{bahcall03a} and references therein). However, both $σ_8\leq 0.7$ and $Ω_\mathrm{m}\leq 0.2$ can be safely ruled out, the best value is when $σ_8=1.0$, $Ω_\mathrm{m}=0.3$ and $ω=-1$. This result is different from that obtained by Bahcall & Bode (\cite{bahcall03a}), who gives $σ_8 =0.98\pm 0.1$ and $Ω_m =0.17\pm 0.05$. For $σ_8=1.0$, higher value of $Ω_\mathrm{m}=0.35$ requires $ω=-2/3$ and $Ω_\mathrm{m}=0.40$ requires $ω=-1/2$.