Cosmological tests with strong gravitational lenses using Gaussian processes

Strong gravitational lenses provide source/lens distance ratios \({\mathcal {D}}_{\mathrm{obs}}\) useful in cosmological tests. Previously, a catalog of 69 such systems was used in a one-on-one comparison between the standard model, \(\varLambda \)CDM, and the \(R_{\mathrm{h}}=ct\) 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 \({\mathcal {D}}_{\mathrm{obs}}\) 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 \(\sim \) 10–30%. These results are still marginal, however, given the relatively small sample. Nonetheless, we conclude that the probability of \(R_{\mathrm{h}}=ct\) being the correct cosmology is somewhat higher than that of \(\varLambda \)CDM, 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 \(R_{\mathrm{h}}=ct\) 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.