# Curve fitting the luminosity distance and redshift data

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## Main Question or Discussion Point

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:

$z = f(d_l)$

mfb
Mentor
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?

mfb
Mentor
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?

kimbyd
Gold Member
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.