A previous analysis of starburst-dominated H II galaxies and H II regions has demonstrated
a statistically significant preference for the Friedmann–Robertson–Walker cosmology with
zero active mass, known as the Rh = ct universe, over cold dark matter (CDM) and its
related dark-matter parametrizations. In this paper, we employ a two-point diagnostic with
these data to present a complementary statistical comparison of Rh = ct with Planck CDM.
Our two-point diagnostic compares, in a pairwise fashion, the difference between the distance
modulus measured at two redshifts with that predicted by each cosmology. Our results support
the conclusion drawn by a previous comparative analysis demonstrating that Rh = ct is
statistically preferred over Planck CDM. But we also find that the reported errors in the
H II measurements may not be purely Gaussian, perhaps due to a partial contamination by
non-Gaussian systematic effects. The use of H II galaxies and H II regions as standard candles
may be improved even further with a better handling of the systematics in these sources.
In this paper, we use an unprecedentedly large sample (158) of confirmed strong lens systems for model selection, comparing five well-studied Friedmann–Robertson–Walker cosmologies: ΛCDM, wCDM (the standard model with a variable dark-energy equation of state), the Rh = ct universe, the (empty) Milne cosmology, and the classical Einstein-de Sitter (matter-dominated) universe. We first use these sources to optimize the parameters in the standard model and show that they are consistent with Planck, though the quality of the best fit is not satisfactory. We demonstrate that this is likely due to underreported errors, or to errors yet to be included in this kind of analysis. We suggest that the missing dispersion may be due to scatter about a pure single isothermal sphere (SIS) model that is often assumed for the mass distribution in these lenses. We then use the Bayes information criterion, with the inclusion of a suggested SIS dispersion, to calculate the relative likelihoods and ranking of these models, showing that Milne and Einstein-de Sitter are completely ruled out, while Rh = ct is preferred over ΛCDM/wCDM with a relative probability of ∼73percent versus ∼24percent. The recently reported sample of new strong lens candidates by the Dark Energy Survey, if confirmed, may be able to demonstrate which of these two models is favoured over the other at a level exceeding 3σ.
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