# The Hubble series: convergence properties and redshift variables

@article{Cattoen2007TheHS,
title={The Hubble series: convergence properties and redshift variables},
author={C'eline Cattoen and Matt Visser},
journal={Classical and Quantum Gravity},
year={2007},
volume={24},
pages={5985-5997}
}
• Published 10 October 2007
• Physics
• Classical and Quantum Gravity
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…
102 Citations

## Figures from this paper

High-Redshift Cosmography
• Physics
• 2010
We constrain the parameters describing the kinematical state of the universe using a cosmographic approach, which is fundamental in that it requires a very minimal set of assumptions (namely to
Constraints on kinematic parameters at z≠0
• Physics
Journal of Cosmology and Astroparticle Physics
• 2018
The standard cosmographic approach consists in performing a series expansion of a cosmological observable around $z=0$ and then using the data to constrain the cosmographic (or kinematic) parameters
Cosmographic Hubble fits to the supernova data
• Physics
• 2008
The Hubble relation between distance and redshift is a purely cosmographic relation that depends only on the symmetries of a Friedmann-Lemaitre-Robertson-Walker spacetime, but does not intrinsically
Redshift evolution of the Amati relation: Calibrated results from the Hubble diagram of quasars at high redshifts
• Physics
Astronomy & Astrophysics
• 2021
Gamma-ray bursts (GRBs) have long been proposed as a complementary probe to type Ia supernovae (SNe Ia) and the cosmic microwave background to explore the expansion history of the high-redshift
Luminosity distance and anisotropic sky-sampling at low redshifts: A numerical relativity study
• Physics
Physical Review D
• 2021
Most cosmological data analysis today relies on the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, providing the basis of the current standard cosmological model. Within this framework,
High-redshift cosmography: auxiliary variables versus Padé polynomials
• Mathematics
• 2020
Cosmography becomes non-predictive when cosmic data span beyond the red shift limit $z\simeq1$. This leads to a \emph{strong convergence issue} that jeopardizes its viability. In this work, we
General cosmography model with spatial curvature
• Physics
Monthly Notices of the Royal Astronomical Society
• 2019
We adopt a cosmographic approach in order to determine spatial curvature (i.e. ΩK), combining the latest release of cosmic chronometer (CC) data, the Pantheon sample of Type Ia supernovae
Cosmographic analysis of dark energy
• Physics
• 2009
The Hubble relation between distance and redshift is a purely cosmographic relation that depends only on the symmetries of a FLRW spacetime, but does not intrinsically make any dynamical assumptions.
Does Hubble tension signal a breakdown in FLRW cosmology?
• Physics
Classical and Quantum Gravity
• 2021
The tension between early and late Universe probes of the Hubble constant has motivated various new FLRW cosmologies. Here, we reanalyse the Hubble tension with a recent age of the Universe
Bounding the Hubble flow in terms of the w parameter
• Physics
• 2008
The last decade has seen increasing efforts to circumscribe and bound the cosmological Hubble flow in terms of model-independent constraints on the cosmological fluid—for instance, the classical

## References

SHOWING 1-10 OF 24 REFERENCES
Cosmography: Extracting the Hubble series from the supernova data
• Physics
• 2007
We perform a number of inter-related cosmographic fits to the legacy05 and gold06 supernova datasets. We pay particular attention to the influence of both statistical and systematic uncertainties,
The Essence of Quintessence and the Cost of Compression
• Physics
• 2004
Standard two-parameter compressions of the infinite dimensional dark energy model space show crippling limitations even with current Type Ia supernova (SN Ia) data unless strong priors are imposed.
Cosmography: Cosmology without the Einstein equations
How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?) These questions are becoming
ACCELERATING UNIVERSES WITH SCALING DARK MATTER
• Physics
• 2000
Friedmann–Robertson–Walker universes with a presently large fraction of the energy density stored in an X-component with wX<-1/3, are considered. We find all the critical points of the system for
The Luminosity Distance, the Equation of State, and the Geometry of the Universe
• Physics
• 1998
The second derivative of the luminosity distance with respect to the redshift is written in terms of the deceleration parameter $q_0$. We point out that the third derivative contains the information
The Supernova Legacy Survey: measurement of Ωm, Ω∧ and w from the first year data set. Commentary
• Physics
• 2006
We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color
Jerk, snap, and the cosmological equation of state
Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological
Type Ia supernova discoveries at z > 1 from the Hubble Space Telescope: Evidence for past deceleration and constraints on dark energy evolution
• Physics
• 2004
We have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to provide the first conclusive evidence for cosmic deceleration that preceded the current
New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy*
• Physics
• 2006
We have discovered 21 new Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to trace the history of cosmic expansion over the last 10 billion yr. These objects,