A comparative analysis of the supernova legacy survey sample with ΛCDM and the R_h = ct universe

The use of Type Ia supernovae (SNe Ia) has thus far produced the most reliable measurement of the expansion history of the universe, suggesting that ΛCDM offers the best explanation for the redshift-luminosity distribution observed in these events. However, analysis of other kinds of sources, 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_h = ct universe is a better fit to the data. The central difficulty with the use of SNe Ia as standard candles is that one must optimize three or four nuisance parameters characterizing supernova (SN) 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 ΛCDM and the R_h = ct universe using the SN Legacy Survey sample of 252 SN events, and show that each model fits its individually reduced data very well. However, since R_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 ΛCDM, 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 using the Bayes Information Criterion that in a pairwise comparison, the likelihood of R_h = ct is ∼90%, compared with only ∼10% for a minimalist form of ΛCDM, in which dark energy is simply a cosmological constant. Compared to R_h = ct, versions of the standard model with more elaborate parametrizations of dark energy are judged to be even less likely.