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    Flux-limited strong gravitational lensing and dark energy

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    In the standard flat cosmological constant (Ξ›\Lambda) cold dark matter (CDM) cosmology, a model of two populations of lens halos for strong gravitational lensing can reproduce the results of the Jodrell-Bank VLA Astrometric Survey (JVAS) and the Cosmic Lens All-Sky Survey (CLASS) radio survey. In such a model, lensing probabilities are sensitive to three parameters: the concentration parameter c1c_1, the cooling mass scale McM_\mathrm{c} and the value of the CDM power spectrum normalization parameter Οƒ8\sigma_8. The value ranges of these parameters are constrained by various observations. However, we found that predicted lensing probabilities are also quite sensitive to the flux density (brightness) ratio qrq_{\mathrm{r}} of the multiple lensing images, which has been, in fact, a very important selection criterion of a sample in any lensing survey experiments. We re-examine the above mentioned model by considering the flux ratio and galactic central Super Massive Black Holes (SMBHs), in flat, low-density cosmological models with different cosmic equations of state Ο‰\omega, and find that the predicted lensing probabilities without considering qrq_{\mathrm{r}} are over-estimated. A low value of qrq_\mathrm{r} can be compensated by raising the cooling mass scale McM_\mathrm{c} in fitting the predicted lensing probabilities to JVAS/CLASS observations. In order to determine the cosmic equation of state Ο‰\omega, the uncertainty in McM_\mathrm{c} must be resolved. The effects of SMBHs cannot be detected by strong gravitational lensing method when qr≀10q_{\mathrm{r}}\leq 10.Comment: 7 pages, 2 figures, corrected to match published version in A&
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