### 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) |
---|---|

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 2013 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

**Cosmic chronometers in the R _{h} = ct universe.** / Melia, Fulvio; Maier, Robert S.

Research output: Contribution to journal › Article

_{h}= ct universe',

*Monthly Notices of the Royal Astronomical Society*, vol. 432, no. 4, pp. 2669-2675. https://doi.org/10.1093/mnras/stt596

}

TY - JOUR

T1 - Cosmic chronometers in the Rh = ct universe

AU - Melia, Fulvio

AU - Maier, Robert S

PY - 2013/10

Y1 - 2013/10

N2 - 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 Rh = 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 Rh =ct Universe fits the data with a reduced χ2 dof = 0.745 for a Hubble constant H0 = 63.2 ± 1.6 km s-1 Mpc-1, and H0 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 χ2 dof values, the AIC yields a likelihood of .82 per cent that the distance.redshift relation of the Rh = 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 (Rh = 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.

AB - 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 Rh = 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 Rh =ct Universe fits the data with a reduced χ2 dof = 0.745 for a Hubble constant H0 = 63.2 ± 1.6 km s-1 Mpc-1, and H0 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 χ2 dof values, the AIC yields a likelihood of .82 per cent that the distance.redshift relation of the Rh = 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 (Rh = 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.

KW - Abundances - galaxies

KW - Evolution - cosmological parameters - cosmology

KW - Methods

KW - Observations - cosmology

KW - Statistical - galaxies

KW - Theory

UR - http://www.scopus.com/inward/record.url?scp=84880014294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880014294&partnerID=8YFLogxK

U2 - 10.1093/mnras/stt596

DO - 10.1093/mnras/stt596

M3 - Article

AN - SCOPUS:84880014294

VL - 432

SP - 2669

EP - 2675

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 4

ER -