Curve fitting the luminosity distance and redshift data

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Discussion Overview

The discussion revolves around the curve fitting of redshift as a function of luminosity distance specifically for type Ia supernovae and gamma-ray bursts. Participants are interested in exploring methods that do not rely on predefined cosmological models, such as the Friedmann–Lemaître–Robertson–Walker (FLRW) metric.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant seeks papers that curve-fit redshift as a function of luminosity distance without assuming a specific model.
  • Another participant argues that some assumptions are necessary for curve fitting, suggesting that a "best fit" function may not yield a realistic representation of the relationship.
  • A different viewpoint suggests that assumptions about the relationship between variables (e.g., linear, exponential) can be made without committing to a specific physical model.
  • One participant notes that common mathematical functions do not provide a good fit quality for the data, indicating that while it is mathematically feasible, the results may not be publishable.
  • There are inquiries about the availability of online repositories for high redshift data suitable for analysis, particularly mentioning supernova data.
  • A participant provides a link to the Supernova Cosmology Project, suggesting it as a source for downloadable data and mentioning the redshift range available in their summary table.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of assumptions for curve fitting and the quality of potential fits. There is no consensus on the best approach to modeling the relationship between redshift and luminosity distance.

Contextual Notes

The discussion highlights limitations regarding the assumptions needed for curve fitting and the challenges in achieving a good fit quality without relying on established cosmological models.

redtree
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Can anyone recommend papers that directly curve-fit redshift as a function of luminosity distance for type Ia supernova and gamma ray bursts? I am looking for papers that do not curve-fit the data via an assumed model, even one as simple as Friedmann–Lemaître–Robertson–Walker (FLRW) metric. I am really just curious to see what the following function ##f## might look like, where ##z## denotes redshift and ##d_l## denotes luminosity distance:

##z = f(d_l) ##
 
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You need some assumptions for f to do curve fitting. The "best fit" is a function that attains the best estimate for z at the best estimate for dl for every single measurement exactly, but that won't give a realistic function.
 
Sure, but the assumptions for ##f## can be about the relationship between the variables (linear? exponential? trigonometric? etc.) without assuming a particular physical model.

Has anyone published the "best fit" function for ##z## as a function of ##d_l## WITHOUT first assuming a particular physical model?
 
Linear, exponential, trigonometric etc. all don't fit. Mathematically you can do it but the fit quality is just too bad to publish it.
 
Is there an online repository of the data out to high ##z## that is downloadable for analysis?
 
redtree said:
Is there an online repository of the data out to high ##z## that is downloadable for analysis?
Depends upon what you mean by high-z. Easiest to work with is probably supernova data. One relatively recent compilation is here, at the Supernova Cosmology Project:
http://supernova.lbl.gov/union/

They have published a summary table of the per-supernova distance/redshift relation:
http://supernova.lbl.gov/union/figures/SCPUnion2.1_mu_vs_z.txt

You'd have to read their papers to understand what the various columns of that table are, to apply them to your own fit. Looks like they go out to a redshift of about 1.4 or so.
 

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