The Age-Redshift Relationship of Old Passive Galaxies

Abstract

We use 32 age measurements of passively evolving galaxies as a function of redshift to test and compare the standard model ($\Lambda$CDM) with the $R_{\mathrm{h}}=ct$ Universe. We show that the latter fits the data with a reduced ${\chi }_{\mathrm{dof}}^2=0.435$ for a Hubble constant $H_0=67.2_{-4.0}^{+4.5}$ km ${\mathrm{s}}^{-1}$ $\mathrm{Mp}{\mathrm{c}}^{-1}$. By comparison, the optimal flat $\Lambda$CDM model, with two free parameters (including ${\Omega }_{\mathrm{m}}=0.12_{-0.11}^{+0.54}$ and $H_0=94.3_{-35.8}^{+32.7}$ km ${\mathrm{s}}^{-1}$ $\mathrm{Mp}{\mathrm{c}}^{-1}$), fits the age-\emph{z} data with a reduced ${\chi }_{\mathrm{dof}}^2=0.428$. Based solely on their ${\chi }_{\mathrm{dof}}^2$ values, both models appear to account for the data very well, though the optimized $\Lambda$CDM parameters are only marginally consistent with those of the concordance model (${\Omega }_{\mathrm{m}}=0.27$ and $H_0=70$ km ${\mathrm{s}}^{-1}$ $\mathrm{Mp}{\mathrm{c}}^{-1}$). Fitting the age-$z$ data with the latter results in a reduced ${\chi }_{\mathrm{dof}}^2=0.523$. However, because of the different number of free parameters in these models, selection tools, such as the Akaike, Kullback and Bayes Information Criteria, favour $R_{\mathrm{h}}=ct$ over $\Lambda$CDM with a likelihood of $\sim 66.5\%-80.5\%$ versus $\sim 19.5\%-33.5\%$. These results are suggestive, though not yet compelling, given the current limited galaxy age-$z$ sample. We carry out Monte Carlo simulations based on these current age measurements to estimate how large the sample would have to be in order to rule out either model at a $\sim 99.7\%$ confidence level. We find that if the real cosmology is $\Lambda$CDM, a sample of $\sim 45$ galaxy ages would be sufficient to rule out $R_{\mathrm{h}}=ct$ at this level of accuracy, while $\sim 350$ galaxy ages would be required to rule out $\Lambda$CDM if the real Universe were instead $R_{\mathrm{h}}=ct$.

arXiv comment36 pages, 13 figures, 1 table; accepted for publication in The Astronomical Journal. arXiv admin note: text overlap with arXiv:1405.2388

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