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### Flux-limited strong gravitational lensing and dark energy

In the standard flat cosmological constant ($\Lambda$) 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 $c_1$, the cooling mass scale $M_\mathrm{c}$ and the
value of the CDM power spectrum normalization parameter $\sigma_8$. 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 $q_{\mathrm{r}}$ 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 $\omega$, and find that the predicted lensing probabilities
without considering $q_{\mathrm{r}}$ are over-estimated. A low value of
$q_\mathrm{r}$ can be compensated by raising the cooling mass scale
$M_\mathrm{c}$ in fitting the predicted lensing probabilities to JVAS/CLASS
observations. In order to determine the cosmic equation of state $\omega$, the
uncertainty in $M_\mathrm{c}$ must be resolved. The effects of SMBHs cannot be
detected by strong gravitational lensing method when $q_{\mathrm{r}}\leq 10$.Comment: 7 pages, 2 figures, corrected to match published version in A&

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