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, ${\sigma }_8$, and the present mass density parameter of the Universe, ${\Omega }_{\mathrm{m}}$, 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 ${\sigma }_8$ or ${\Omega }_{\mathrm{m}}$ as a free parameter to be constrained by data. Another varying parameter is 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 ${\Omega }_{\mathrm{m}}$ in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: ${\sigma }_8{\Omega }_{\mathrm{m}}^{0.6}\approx 0.33$ (Bahcall & Bode\cite{bahcall03a} and references therein). However, both ${\sigma }_8\le 0.7$ and ${\Omega }_{\mathrm{m}}\le 0.2$ can be safely ruled out, the best value is when ${\sigma }_8=1.0$, ${\Omega }_{\mathrm{m}}=0.3$ and $\omega =-1$. This result is different from that obtained by Bahcall & Bode (\cite{bahcall03a}), who gives ${\sigma }_8=0.98\pm 0.1$ and ${\Omega }_m=0.17\pm 0.05$. For ${\sigma }_8=1.0$, higher value of ${\Omega }_{\mathrm{m}}=0.35$ requires $\omega =-2/3$ and ${\Omega }_{\mathrm{m}}=0.40$ requires $\omega =-1/2$.

9 pages, 4 figures, references updated

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