I have several questions about the process of determining the value of cosmological parameters by LMS fitting tunctions of the form z = f(D(adsbygoogle = window.adsbygoogle || []).push({}); _{L}) (where D_{L}is the luminosity distance to astronomical data points), for example, as shown in the following diagram:

The five cosmological parameters I am thinking of are: H_{0}, and the four density ratios (which sum to unity).

To set the context for my questions, I first present my (possiibly incorrect) assumptions about the process.

The particular z = f(D_{L}) function for one model would be somehow based on the function

t = t(a) = t (1+z) calculated from the Friedmann equation

with selected values for the five parameters, h0 and the four Ωs which sum to unity. For each set of five parameters, a badness of fit measure B is calculated (i.e., the weighted sum of the squares of differences between the acutal astronomical values (the dots in the diagram)) and he corresponding points on the z = f(D_{L}) curve . The values of the five parameters that result in the smallest value for B are then the values that have been determined by the astronomical data. The weights used the calulate B are the recipricals of the widths (distance error ranges) of the horizontal observational errors bars for each data point.

Questions:

(a) Are my assumptions OK?

(b) What is the form of the z = f(D_{L}) function in terms of a model's t(1+z) function.

(c) While I have seen values with error ranges published for the parameters, I have not seen any values given for the probability that a given parameter is significantly different than zero, (that is some kind of statistical test showing the probability that the null-hypothesis is false). Does anyone know if someone has done such a calculation?

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# Fitting a model to astronomical data

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