REVIEW
Bayesian analysis of Friedmannless cosmologies
Astrophysics · Submitted 2 Mar 2006 · 21 references
Pith's verdict: A useful, modest Bayesian model-comparison paper that makes a defensible negative point about redshift-dependent deceleration, though the SNLS evidence numbers are profile quantities, not full Bayes factors.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
Supernova data give no significant evidence of a transition from deceleration to acceleration; a constant, negative deceleration parameter suffices.
The reading
What carries the argument
The central object is the deceleration parameter $q \equiv -\ddot{a}/(aH^2)$ written as a function of redshift and converted into a prediction for supernova magnitudes through the luminosity distance $d_L(z)=(1+z)\,\mathrm{sinn}_k\!\left(\int_0^z du/H(u)\right)$. Eight parameterizations are compared: constant $q$, polynomials in $z$, expansions in powers of $(1+z)^{-3i}$, a two-bin piecewise-constant transition model, and their non-flat versions. Model comparison is done with the Bayesian evidence $E(M)=\int d\theta\,P(D|\theta,M)P(\theta|M)$ under wide top-hat priors, with Bayes factors judged on the Jeffreys scale. This machinery automatically penalizes extra parameters, so a redshift-dependent $q$ is preferred only if its gain in likelihood outweighs the cost of its larger prior volume.
Extended reading notes
Core claim
The paper's central claim is that the Gold and SNLS supernova samples are fully consistent with a constant deceleration parameter $q_0 \approx -0.3$ to $-0.4$, and that no redshift-dependent parameterization of $q$ is significantly preferred once model complexity is penalized by the Bayesian evidence. In the model ranking, the best model for both data sets is $q(z)=\mathrm{const}$; the two-bin transition model, which treats the deceleration-to-acceleration redshift as a free parameter, is not favored. The paper therefore argues that the commonly quoted transition redshift is most likely an artifact of the linear parameterization of $q(z)$, which forces a transition whenever the fitted coefficients have opposite signs. The robust statement the data support is only that the present deceleration parameter is negative.
Load-bearing premise
The SNLS sample's evidence calculation holds the three calibration parameters (stretch, color, and overall magnitude offset) at their best-fit values instead of integrating over them; if those parameters are correlated with the model parameters, the model ranking could shift.
Editorial extensions
If this is right
- If the claim is correct, the only robust kinematic statement from Type Ia supernova data is that the current deceleration parameter is negative; no measurable redshift dependence is required.
- Published transition redshifts such as $z_t \approx 0.46$ should not be read as evidence for when acceleration began, because the linear model that produces them forces a transition whenever $q_0$ and $q_1$ have opposite signs.
- The two-bin transition model M5 is not favored by either data set, so the data cannot currently say when, or whether, the universe went from deceleration to acceleration.
- The Gold and SNLS samples rank the models differently, so conclusions about the expansion history depend on which sample is used.
- Ranking by the Bayesian Information Criterion disagrees with the full Bayesian evidence ranking, so shortcut model-selection criteria can be misleading in this setting.
Reading between the lines
- Repeating this evidence comparison on later, larger supernova compilations, ideally with the calibration nuisance parameters marginalized rather than fixed, would test whether the constant-$q$ verdict survives; the paper itself notes that fixing or marginalizing nuisance parameters changes some Bayes factors.
- The result suggests that dark-energy claims based on supernova fits alone, such as equation-of-state values below $-1$, are kinematically underdetermined: the same data support a one-parameter constant-$q$ description.
- A natural extension is to combine supernova data with other expansion-history probes, such as cosmic microwave background or baryon acoustic oscillation measurements, to see whether any redshift dependence of $q$ emerges when the expansion history is pinned down more tightly.
- The disagreement between the two samples' rankings implies that future claims of a measured transition redshift should be backed by model selection, not just by a best-fit parameter value.
Original abstract
Assuming only a homogeneous and isotropic universe and using both the 'Gold' Supernova Type Ia sample of Riess et al. and the results from the Supernova Legacy Survey, we calculate the Bayesian evidence of a range of different parameterizations of the deceleration parameter. We consider both spatially flat and curved models. Our results show that although there is strong evidence in the data for an accelerating universe, there is little evidence that the deceleration parameter varies with redshift.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Assuming only a homogeneous and isotropic universe and using both the 'Gold' Supernova Type Ia sample of Riess et al. and the results from the Supernova Legacy Survey, we calculate the Bayesian evidence of a range of different parameterizations of the deceleration parameter. We consider both spatially flat and curved models. Our results show that although there is strong evidence in the data for an accelerating universe, there is little evidence that the deceleration parameter varies with redshift.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Assuming only a homogeneous and isotropic universe and using both the 'Gold' Supernova Type Ia sample of Riess et al. and the results from the Supernova Legacy Survey, we calculate the Bayesian evidence of a range of different parameterizations of the deceleration parameter. | method 0.85 | 0.94 | 0.05 | asserted 0.91 |
| s1 | We consider both spatially flat and curved models. | method 0.88 | 0.62 | 0.02 | asserted 0.90 |
| s2 | Our results show that although there is strong evidence in the data for an accelerating universe, there is little evidence that the deceleration parameter varies with redshift. | result 0.99 | 0.96 | 0.92 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:astro-ph/0603053 by the authors.
References
How the literature uses it
4 arXiv papers cite this in 7 sentences
Papers citing it · 5 sentences without a confident label
Builds on it 1 paper
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In the next section we describe the WFR method, a generalization of the procedure applied in [ref] which is able to mitigate even more the problem, and to go one step further concerning the model-independence of these kind of analyses.
Quantifying the evidence for the current speed-up of the Universe with low and intermediate-redshift data. A more model-independent approach · Estimation of $q_0$ in some model and parametrization-dependent scenarios, and the need of an improved cosmographical ap · 0.87
Cites it as background 1 paper
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Many other authors have used different data sets such as Gamma Ray Bursts (GRBs), Hubble Observational Data $H(z)$, BAO, CMB, Galaxy Clusters , lookback time etc. to reconstruct $q(z)$ or to constrain the transition redshift [ref] .
Transition Redshift: New constraints from parametric and nonparametric methods · Introduction · 0.95
Discussion
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