The Hubble series: Convergence properties and redshift variables
| dc.creator | Cattoen, Celine | |
| dc.creator | Visser, Matt | |
| dc.date | 2007-10-10 | |
| dc.date.accessioned | 2026-07-07T10:57:36Z | |
| dc.date.available | 2026-07-07T10:57:36Z | |
| dc.description | In cosmography, cosmokinetics, and cosmology it is quite common to encounter physical quantities expanded as a Taylor series in the cosmological redshift z. Perhaps the most well-known exemplar of this phenomenon is the Hubble relation between distance and redshift. However, we now have considerable high-z data available, for instance we have supernova data at least back to redshift z=1.75. This opens up the theoretical question as to whether or not the Hubble series (or more generally any series expansion based on the z-redshift) actually converges for large redshift? Based on a combination of mathematical and physical reasoning, we argue that the radius of convergence of any series expansion in z is less than or equal to 1, and that z-based expansions must break down for z>1, corresponding to a universe less than half its current size. Furthermore, we shall argue on theoretical grounds for the utility of an improved parameterization y=z/(1+z). In terms of the y-redshift we again argue that the radius of convergence of any series expansion in y is less than or equal to 1, so that y-based expansions are likely to be good all the way back to the big bang y=1, but that y-based expansions must break down for y<-1, now corresponding to a universe more than twice its current size. | |
| dc.description | 15 pages, 2 figures, accepted for publication in Classical and Quantum Gravity | |
| dc.identifier | https://arxiv.org/abs/0710.1887 | |
| dc.identifier | http://arxiv.org/abs/0710.1887 | |
| dc.identifier | Class.Quant.Grav.24:5985-5998,2007 | |
| dc.identifier | doi:10.1088/0264-9381/24/23/018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/186811 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | The Hubble series: Convergence properties and redshift variables | |
| dc.type | text |