Cosmological Tests With Strong Gravitational Lenses using Gaussian
  Processes
  Strong gravitational lenses provide source/lens distance ratios D_obs useful
in cosmological tests. Previously, a catalog of 69 such systems was used in a
one-on-one comparison between the standard model, LCDM, and the R_h=ct
universe, which has thus far been favored by the application of model selection
tools to many other kinds of data. But in that work, the use of model
parametric fits to the observations could not easily distinguish between these
two cosmologies, in part due to the limited measurement precision. Here, we
instead use recently developed methods based on Gaussian Processes (GP), in
which D_obs may be reconstructed directly from the data without assuming any
parametric form. This approach not only smooths out the reconstructed function
representing the data, but also reduces the size of the 1-sigma confidence
regions, thereby providing greater power to discern between different models.
With the current sample size, we show that analyzing strong lenses with a GP
approach can definitely improve the model comparisons, producing probability
differences in the range ~10-30%. These results are still marginal, however,
given the relatively small sample. Nonetheless, we conclude that the
probability of R_h=ct being the correct cosmology is somewhat higher than that
of LCDM, with a degree of significance that grows with the number of sources in
the subsamples we consider. Future surveys will significantly grow the catalog
of strong lenses and will therefore benefit considerably from the GP method we
describe here. In addition, we point out that if the R_h=ct universe is
eventually shown to be the correct cosmology, the lack of free parameters in
the study of strong lenses should provide a remarkably powerful tool for
uncovering the mass structure in lensing galaxies.
