### Abstract

Unlike other observational signatures in cosmology, the angular-diameter distance d_{A}(z) uniquely reaches a maximum (at z_{max}) and then shrinks to zero towards the big bang. The location of this turning point depends sensitively on the model, but has been difficult to measure. In this paper, we estimate and use z_{max} inferred from quasar cores: (1) by employing a sample of 140 objects yielding a much reduced dispersion due to pre-constrained limits on their spectral index and luminosity, (2) by reconstructing d_{A}(z) using Gaussian processes, and (3) comparing the predictions of seven different cosmologies and showing that the measured value of z_{max} can effectively discriminate between them. We find that z_{max} = 1.70 ± 0.20 - an important new probe of the Universe's geometry. The most strongly favoured model is R_{h} = ct, followed by PlanckΛCDM. Several others, including Milne, Einstein-de Sitter, and Static tired light are strongly rejected. According to these results, the R_{h} = ct universe, which predicts z_{max} = 1.718, has a ~92.8 per cent probability of being the correct cosmology. For consistency, we also carry out model selection based on d_{A}(z) itself. This test confirms that R_{h} = ct and PlanckΛCDM are among the few models that account for angular-size data better than those that are disfavoured by z_{max}. The d_{A}(z) comparison, however, is less discerning than that with z_{max}, due to the additional free parameter, H_{0}.We find that H_{0} = 63.4 ± 1.2 km s^{-1} Mpc^{-1} for R_{h} = ct, and 69.9 ± 1.5 km s^{-1} Mpc^{-1} for ΛCDM. Both are consistent with previously measured values in each model, though they differ from each other by over 4σ. In contrast, model selection based on z_{max} is independent of H_{0}.

Original language | English (US) |
---|---|

Pages (from-to) | 2144-2152 |

Number of pages | 9 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 480 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1 2018 |

### Fingerprint

### Keywords

- Cosmological parameters
- Cosmology: observations
- Cosmology: theory
- Distance scale
- Galaxies: active

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Monthly Notices of the Royal Astronomical Society*,

*480*(2), 2144-2152. https://doi.org/10.1093/MNRAS/STY1962

**The maximum angular-diameter distance in cosmology.** / Melia, Fulvio; Yennapureddy, Manoj K.

Research output: Contribution to journal › Article

*Monthly Notices of the Royal Astronomical Society*, vol. 480, no. 2, pp. 2144-2152. https://doi.org/10.1093/MNRAS/STY1962

}

TY - JOUR

T1 - The maximum angular-diameter distance in cosmology

AU - Melia, Fulvio

AU - Yennapureddy, Manoj K.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Unlike other observational signatures in cosmology, the angular-diameter distance dA(z) uniquely reaches a maximum (at zmax) and then shrinks to zero towards the big bang. The location of this turning point depends sensitively on the model, but has been difficult to measure. In this paper, we estimate and use zmax inferred from quasar cores: (1) by employing a sample of 140 objects yielding a much reduced dispersion due to pre-constrained limits on their spectral index and luminosity, (2) by reconstructing dA(z) using Gaussian processes, and (3) comparing the predictions of seven different cosmologies and showing that the measured value of zmax can effectively discriminate between them. We find that zmax = 1.70 ± 0.20 - an important new probe of the Universe's geometry. The most strongly favoured model is Rh = ct, followed by PlanckΛCDM. Several others, including Milne, Einstein-de Sitter, and Static tired light are strongly rejected. According to these results, the Rh = ct universe, which predicts zmax = 1.718, has a ~92.8 per cent probability of being the correct cosmology. For consistency, we also carry out model selection based on dA(z) itself. This test confirms that Rh = ct and PlanckΛCDM are among the few models that account for angular-size data better than those that are disfavoured by zmax. The dA(z) comparison, however, is less discerning than that with zmax, due to the additional free parameter, H0.We find that H0 = 63.4 ± 1.2 km s-1 Mpc-1 for Rh = ct, and 69.9 ± 1.5 km s-1 Mpc-1 for ΛCDM. Both are consistent with previously measured values in each model, though they differ from each other by over 4σ. In contrast, model selection based on zmax is independent of H0.

AB - Unlike other observational signatures in cosmology, the angular-diameter distance dA(z) uniquely reaches a maximum (at zmax) and then shrinks to zero towards the big bang. The location of this turning point depends sensitively on the model, but has been difficult to measure. In this paper, we estimate and use zmax inferred from quasar cores: (1) by employing a sample of 140 objects yielding a much reduced dispersion due to pre-constrained limits on their spectral index and luminosity, (2) by reconstructing dA(z) using Gaussian processes, and (3) comparing the predictions of seven different cosmologies and showing that the measured value of zmax can effectively discriminate between them. We find that zmax = 1.70 ± 0.20 - an important new probe of the Universe's geometry. The most strongly favoured model is Rh = ct, followed by PlanckΛCDM. Several others, including Milne, Einstein-de Sitter, and Static tired light are strongly rejected. According to these results, the Rh = ct universe, which predicts zmax = 1.718, has a ~92.8 per cent probability of being the correct cosmology. For consistency, we also carry out model selection based on dA(z) itself. This test confirms that Rh = ct and PlanckΛCDM are among the few models that account for angular-size data better than those that are disfavoured by zmax. The dA(z) comparison, however, is less discerning than that with zmax, due to the additional free parameter, H0.We find that H0 = 63.4 ± 1.2 km s-1 Mpc-1 for Rh = ct, and 69.9 ± 1.5 km s-1 Mpc-1 for ΛCDM. Both are consistent with previously measured values in each model, though they differ from each other by over 4σ. In contrast, model selection based on zmax is independent of H0.

KW - Cosmological parameters

KW - Cosmology: observations

KW - Cosmology: theory

KW - Distance scale

KW - Galaxies: active

UR - http://www.scopus.com/inward/record.url?scp=85055323463&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055323463&partnerID=8YFLogxK

U2 - 10.1093/MNRAS/STY1962

DO - 10.1093/MNRAS/STY1962

M3 - Article

AN - SCOPUS:85055323463

VL - 480

SP - 2144

EP - 2152

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 2

ER -