# Astrophysical Tests of Kinematical Conformal Cosmology in Fourth-Order Conformal Weyl Gravity

## Abstract

**:**

## 1. Introduction

## 2. Conformal Gravity and Kinematical Conformal Cosmology

## 3. KCC and Type Ia Supernovae

- (1)
- f is some arbitrary function of $(1+z)$, with a “fixed point” at 1, that is, $f\left(1\right)=1$, or ${lim}_{z\to 0}\phantom{\rule{4pt}{0ex}}f(1+z)=1$.
- (2)
- (3)
- f is a function possibly built out of other expressions of KCC, which also depend on the factor $(1+z)$.

#### 3.1. SNIa Data Fitting

#### 3.2. Union 2.1 Data and KCC Plots

**Figure 1.**Data from Union 2.1 SNIa set [35] are fitted with Equation (25). Our KCC fits (red-solid for fixed α and β; black long-dashed for variable α and β) show very good statistical quality (${R}^{2}=0.996$) and are very close to the standard cosmology prediction (SC, blue short-dashed). Also shown (dotted-green curves) is the range of our KCC fitting curves for a variable $\alpha =1.9-2.1$.

**Figure 2.**The same data and fitting curves presented in Figure 1 are shown here in a standard Hubble plot, with logarithmic axis for the redshift z. The meaning of the symbols and of the different plots is the same as in the previous figure.

**Figure 4.**A subset of Union 2.1 SNIa data [35], for $z\lesssim 0.1$, is fitted with Equation (38). Our low-z KCC fits (red-solid curves for fixed α; black long-dashed curves for variable α) yield essentially the same results as in the previous fits, which used the full range of values for z. Also shown are the ranges of our KCC fitting curves, for a variable $\alpha =1.9-2.1$ (green-dotted curves) and for a variable $\delta =(3.00-4.00)\times {10}^{-5}$ (blue, short-dashed curves).

## 4. KCC and Hubble Parameter Data

**Table 1.**Available Hubble parameter data H(z), from various sources, obtained with different methods.

z | $H\left(z\right)\phantom{\rule{4pt}{0ex}}(km\phantom{\rule{4pt}{0ex}}{s}^{-1}\phantom{\rule{4pt}{0ex}}{\mathrm{Mpc}}^{-1})$ | Source | Method (See Text) |
---|---|---|---|

0.0900 | 69 ± 12 | Jimenez et al. (2003) [40] | DA |

0.1700 | 83 ± 8 | Simon et al. (2005) [41] | DA |

0.2700 | 77 ± 14 | Simon et al. (2005) [41] | DA |

0.4000 | 95 ± 17 | Simon et al. (2005) [41] | DA |

0.9000 | 117 ± 23 | Simon et al. (2005) [41] | DA |

1.3000 | 168 ± 17 | Simon et al. (2005) [41] | DA |

1.4300 | 177 ± 18 | Simon et al. (2005) [41] | DA |

1.5300 | 140 ± 14 | Simon et al. (2005) [41] | DA |

1.7500 | 202 ± 40 | Simon et al. (2005) [41] | DA |

0.4800 | 97 ± 62 | Stern et al. (2010) [42] | DA |

0.8800 | 90 ± 40 | Stern et al. (2010) [42] | DA |

0.1791 | 75 ± 4 | Moresco et al. (2012) [38] | DA |

0.1993 | 75 ± 5 | Moresco et al. (2012) [38] | DA |

0.3519 | 83 ± 14 | Moresco et al. (2012) [38] | DA |

0.5929 | 104 ± 13 | Moresco et al. (2012) [38] | DA |

0.6797 | 92 ± 8 | Moresco et al. (2012) [38] | DA |

0.7812 | 105 ± 12 | Moresco et al. (2012) [38] | DA |

0.8754 | 125 ± 17 | Moresco et al. (2012) [38] | DA |

1.0370 | 154 ± 20 | Moresco et al. (2012) [38] | DA |

0.2400 | 79.69 ± 2.65 | Gazta$\tilde{n}$aga et al. (2009) [39] | BAO |

0.4300 | 86.45 ± 3.68 | Gazta$\tilde{n}$aga et al. (2009) [39] | BAO |

0.0700 | 69 ± 19.6 | Zhang et al. (2012) [43] | DA |

0.1200 | 68.6 ± 26.2 | Zhang et al. (2012) [43] | DA |

0.2000 | 72.9 ± 29.6 | Zhang et al. (2012) [43] | DA |

0.2800 | 88.8 ± 36.6 | Zhang et al. (2012) [43] | DA |

0.4400 | 82.6 ± 7.8 | Blake et al. (2012) [44] | BAO and GC |

0.6000 | 97.9 ± 6.1 | Blake et al. (2012) [44] | BAO and GC |

0.7300 | 97.3 ± 7.0 | Blake et al. (2012) [44] | BAO and GC |

0.3500 | 82.1 ± 5 | Chuang et al. (2012) [45] | GC |

**Table 2.**Standard Cosmology and KCC estimates for the age of the Universe and of quasar APM 08279+5255.

Model | Age of Universe | Age of Quasar |
---|---|---|

SC (${\Omega}_{M}\cong 0.3$, ${\Omega}_{\Lambda}\cong 0.7$, ${\mathbf{H}}_{0}=67.3\phantom{\rule{4pt}{0ex}}km\phantom{\rule{4pt}{0ex}}{s}^{-1}\phantom{\rule{4pt}{0ex}}{\mathrm{Mpc}}^{-1}$) | 14.0 Gyr | 1.34 Gyr |

KCC—parameters from Equation (43) | 14.2 Gyr | 1.65 Gyr |

KCC—parameters from Equation (44) | 15.8 Gyr | 2.45 Gyr |

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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Varieschi, G.U.
Astrophysical Tests of Kinematical Conformal Cosmology in Fourth-Order Conformal Weyl Gravity. *Galaxies* **2014**, *2*, 577-600.
https://doi.org/10.3390/galaxies2040577

**AMA Style**

Varieschi GU.
Astrophysical Tests of Kinematical Conformal Cosmology in Fourth-Order Conformal Weyl Gravity. *Galaxies*. 2014; 2(4):577-600.
https://doi.org/10.3390/galaxies2040577

**Chicago/Turabian Style**

Varieschi, Gabriele U.
2014. "Astrophysical Tests of Kinematical Conformal Cosmology in Fourth-Order Conformal Weyl Gravity" *Galaxies* 2, no. 4: 577-600.
https://doi.org/10.3390/galaxies2040577