A COMPARISON OF COSMOLOGICAL MODELS USING STRONG GRAVITATIONAL LENSING GALAXIES

Abstract

Strongly gravitationally lensed quasar-galaxy systems allow us to compare competing cosmologies as long as one can be reasonably sure of the mass distribution within the intervening lens. In this paper, we assemble a catalog of 69 such systems from the Sloan Lens ACS and Lens Structure and Dynamics surveys suitable for this analysis, and carry out a one-on-one comparison between the standard model, $\Lambda$CDM, and the $R_{\rm h}=ct$ Universe, which has thus far been favored by the application of model selection tools to other kinds of data. We find that both models account for the lens observations quite well, though the precision of these measurements does not appear to be good enough to favor one model over the other. Part of the reason is the so-called bulge-halo conspiracy that, on average, results in a baryonic velocity dispersion within a fraction of the optical effective radius virtually identical to that expected for the whole luminous-dark matter distribution modeled as a singular isothermal ellipsoid, though with some scatter among individual sources. Future work can greatly improve the precision of these measurements by focusing on lensing systems with galaxies as close as possible to the background sources. Given the limitations of doing precision cosmological testing using the current sample, we also carry out Monte Carlo simulations based on the current lens measurements to estimate how large the source catalog would have to be in order to rule out either model at a $\sim 99.7\%$ confidence level. We find that if the real cosmology is $\Lambda$CDM, a sample of $\sim 200$ strong gravitational lenses would be sufficient to rule out $R_{\rm h}=ct$ at this level of accuracy, while $\sim 300$ strong gravitational lenses would be required to rule out $\Lambda$CDM if the real Universe were instead $R_{\rm h}=ct$. The difference in required sample size reflects the greater number of free parameters available to fit the data with $\Lambda$CDM. We point out that, should the $R_{\rm h}=ct$ Universe eventually emerge as the correct cosmology, its lack of any free parameters for this kind of work will provide a remarkably powerful probe of the mass structure in lensing galaxies, and a means of better understanding the origin of the bulge-halo conspiracy.