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The use of time-delay gravitational lenses to examine the cosmologicalexpansion introduces a new standard ruler with which to test theoreticalmodels. The sample suitable for this kind of work now includes 12 lens systems,which have thus far been used solely for optimizing the parameters of$\Lambda$CDM. In this paper, we broaden the base of support for this new,important cosmic probe by using these observations to carry out a one-on-onecomparison between {\it competing} models. The currently available sampleindicates a likelihood of $\sim 70-80%$ that the $R_{\rm h}=ct$ Universe is thecorrect cosmology versus $\sim 20-30%$ for the standard model. This possiblyinteresting result reinforces the need to greatly expand the sample oftime-delay lenses, e.g., with the successful implementation of the Dark EnergySurvey, the VST ATLAS survey, and the Large Synoptic Survey Telescope. Inanticipation of a greatly expanded catalog of time-delay lenses identified withthese surveys, we have produced synthetic samples to estimate how large theywould have to be in order to rule out either model at a $\sim 99.7%$ confidencelevel. We find that if the real cosmology is $\Lambda$CDM, a sample of $\sim150$ time-delay lenses would be sufficient to rule out $R_{\rm h}=ct$ at thislevel of accuracy, while $\sim 1,000$ time-delay lenses would be required torule out $\Lambda$CDM if the real Universe is instead $R_{\rm h}=ct$. Thisdifference in required sample size reflects the greater number of freeparameters available to fit the data with $\Lambda$CDM.

A Comparison of Cosmological Models Using Time Delay Lenses