A Comparative Analysis of the Supernova Legacy Survey Sample with
  {\Lambda}CDM and the $R_{\rm h}=ct$ Universe
  The use of Type~Ia SNe has thus far produced the most reliable measurement of
the expansion history of the Universe, suggesting that $\Lambda$CDM offers the
best explanation for the redshift--luminosity distribution observed in these
events. But the analysis of other kinds of source, such as cosmic chronometers,
gamma ray bursts, and high-$z$ quasars, conflicts with this conclusion,
indicating instead that the constant expansion rate implied by the $R_{\rm
h}=ct$ Universe is a better fit to the data. The central difficulty with the
use of Type~Ia SNe as standard candles is that one must optimize three or four
nuisance parameters characterizing supernova luminosities simultaneously with
the parameters of an expansion model. Hence in comparing competing models, one
must reduce the data independently for each. We carry~out such a comparison of
$\Lambda$CDM and the $R_{\rm h}=ct$ Universe, using the Supernova Legacy Survey
(SNLS) sample of 252 SN~events, and show that each model fits its individually
reduced data very well. But since $R_{\rm h}=ct$ has only one free parameter
(the Hubble constant), it follows from a standard model selection technique
that it is to be preferred over $\Lambda$CDM, the minimalist version of which
has three (the Hubble constant, the scaled matter density and either the
spatial curvature constant or the dark-energy equation-of-state parameter). We
estimate by the Bayes Information Criterion that in a pairwise comparison, the
likelihood of $R_{\rm h}=ct$ is $\sim 90\%$, compared with only $\sim 10\%$ for
a minimalist form of $\Lambda$CDM, in which dark energy is simply a
cosmological constant. Compared to $R_{\rm h}=ct$, versions of the standard
model with more elaborate parametrizations of dark energy are judged to be even
less likely.
