### Abstract

The use of luminous red galaxies as cosmic chronometers provides us with an indispensable method of measuring the universal expansion rate H(z) in a model-independent way. Unlike many probes of the cosmological history, this approach does not rely on integrated quantities, such as the luminosity distance, and therefore does not require the pre-assumption of any particular model, which may bias subsequent interpretations of the data. We employ three statistical tools . the Akaike, Kullback and Bayes Information Criteria (AIC, KIC and BIC) . to compare the δ cold dark matter (δCDM) model and the R_{h} = ct Universe with the currently available measurements of H(z), and show that the Rh = ct Universe is favoured by these model selection criteria. The parameters in each model are individually optimized by maximum likelihood estimation. The R_{h} =ct Universe fits the data with a reduced χ^{2} dof = 0.745 for a Hubble constant H0 = 63.2 ± 1.6 km s^{-1} Mpc^{-1}, and H_{0} is the sole parameter in this model. By comparison, the optimal δCDM model, which has three free parameters (including H0 = 68.9 ± 3.3 km s.1 Mpc.1, σm = 0.32, and a dark-energy equation of state pde =-ρde), fits the H(z) data with a reduced χ2 dof = 0.777. With these χ^{2} dof values, the AIC yields a likelihood of .82 per cent that the distance.redshift relation of the R_{h} = ct Universe is closer to the correct cosmology, than is the case for δCDM. If the alternative BIC criterion is used, the respective Bayesian posterior probabilities are 91.2 per cent (R_{h} = ct) versus 8.8 per cent (δCDM). Using the concordance δCDM parameter values, rather than those obtained by fitting δCDM to the cosmic chronometer data, would further disfavour δCDM.

Original language | English (US) |
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Pages (from-to) | 2669-2675 |

Number of pages | 7 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 432 |

Issue number | 4 |

DOIs | |

State | Published - Oct 1 2013 |

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### Keywords

- Abundances - galaxies
- Evolution - cosmological parameters - cosmology
- Methods
- Observations - cosmology
- Statistical - galaxies
- Theory

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science