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(l), the cooling mass scale M, 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(r) of the multiple lensing images, which has been a very important selection criterion of a sample in any lensing survey experiments. We re-examine the mentioned above 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 w, and find that the predicted lensing probabilities without considering q(r) are over-estimated. A low value of q(r) can be compensated for by raising the cooling mass scale M-c in fitting the predicted lensing probabilities to JVAS/CLASS observations. To determine the cosmic equation of state w, the uncertainty in M-c must be resolved. The effects of SMBHs cannot be detected by strong gravitational lensing methods when q(r) less than or equal to 10.