# Curve fitting the luminosity distance and redshift data

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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) ##

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.

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?

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.

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