We continue to build support for the proposal to use H ii galaxies ( HIIGx ) and giant extragalactic H ii regions ( GEHR ) as standard candles to construct the Hubble diagram at redshifts beyond the current reach of Type Ia supernovae .
Using a sample of 25 high-redshift HIIGx , 107 local HIIGx , and 24 GEHR , we confirm that the correlation between the emission-line luminosity and ionized-gas velocity dispersion is a viable luminosity indicator , and use it to test and compare the standard model \Lambda CDM and the R _ { h } = ct Universe by optimizing the parameters in each cosmology using a maximization of the likelihood function .
For the flat \Lambda CDM model , the best fit is obtained with \Omega _ { m } = 0.40 _ { -0.09 } ^ { +0.09 } .
However , statistical tools , such as the Akaike ( AIC ) , Kullback ( KIC ) and Bayes ( BIC ) Information Criteria favor R _ { h } = ct over the standard model with a likelihood of \approx 94.8 \% - 98.8 \% versus only \approx 1.2 \% - 5.2 \% .
For w CDM ( the version of \Lambda CDM with a dark-energy equation of state w _ { de } \equiv p _ { de } / \rho _ { de } rather than w _ { de } = w _ { \Lambda } = -1 ) , a statistically acceptable fit is realized with \Omega _ { m } = 0.22 _ { -0.14 } ^ { +0.16 } and w _ { de } = -0.51 _ { -0.25 } ^ { +0.15 } which , however , are not fully consistent with their concordance values .
In this case , w CDM has two more free parameters than R _ { h } = ct , and is penalized more heavily by these criteria .
We find that R _ { h } = ct is strongly favored over w CDM with a likelihood of \approx 92.9 \% - 99.6 \% versus only 0.4 \% - 7.1 \% .
The current HIIGx sample is already large enough for the BIC to rule out \Lambda CDM/ w CDM in favor of R _ { h } = ct at a confidence level approaching 3 \sigma .