# Curve fitting the luminosity distance and redshift data

• I
• redtree
In summary, the conversation is about finding papers that directly curve-fit redshift as a function of luminosity distance without assuming a particular physical model. The function in question is denoted by ##z = f(d_l)## and the goal is to see what this function might look like. However, it is noted that using linear, exponential, or trigonometric functions do not provide a good fit. The conversation also mentions an online repository of data for analysis, with the suggestion of using supernova data from the Supernova Cosmology Project. This data goes out to a redshift of approximately 1.4.

#### 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) ##

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.