The Hubble series: Convergence properties and redshift variables

dc.creatorCattoen, Celine
dc.creatorVisser, Matt
dc.date2007-10-10
dc.date.accessioned2026-07-07T10:57:36Z
dc.date.available2026-07-07T10:57:36Z
dc.descriptionIn 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.description15 pages, 2 figures, accepted for publication in Classical and Quantum Gravity
dc.identifierhttps://arxiv.org/abs/0710.1887
dc.identifierhttp://arxiv.org/abs/0710.1887
dc.identifierClass.Quant.Grav.24:5985-5998,2007
dc.identifierdoi:10.1088/0264-9381/24/23/018
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/186811
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleThe Hubble series: Convergence properties and redshift variables
dc.typetext

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