Curve fitting the luminosity distance and redshift data

[redtree]

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]

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 d_l for every single measurement exactly, but that won't give a realistic function.

 

[redtree]

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]

Linear, exponential, trigonometric etc. all don't fit. Mathematically you can do it but the fit quality is just too bad to publish it.

 

[redtree]

Is there an online repository of the data out to high $z$ that is downloadable for analysis?

 

[kimbyd]

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.