What is the purpose of Cosmology ?

This post is an attempt to ask what is the purpose of Cosmology. The context arises from some discussions I've been having on the OU science fora about the so called Big bang. It is apparent that some people there seem to want Cosmology to explain more than it can. One correspondent in particular seemed to think that it was ill defined, something with which I quite disagree also he and some others seemed to subscribe to the view that there was a conspiracy to prevent debate about other alternatives. So lets start with what physicists mean by the big bang. It is actually a combination of particular models deriving from fundamental theories the synthesis finally arising in the mid-sixties. So what are the components

1) The Friedmann model of the expansion of the universe which is a consequence of the Robertson Walker metric which is one of the many possible solutions of Einstein's Field equations of General Relativity

2) Fermi's theory of the Weak interaction which is now part of the Standard Model of particle physics itself one of many particular quantum field theories

3) Relativistic Statistical physics which when coupled with 1 gives rise to expressions which govern the temperature of the universe as a function of time.

4) A very detailed chain of nuclear fusion reactions which is responsible for the relative abundances of the light elements from this the correct hydrogen and helium abundance something which the steady state models of cosmology could not predict accurately. However Gamow's original hope that the abundance of all elements could be derived from this chain turned out not to be correct as the chain stops at iron. It is now known that the other elements are produced from stellar explosions.

This synthesis was achieved by Peebles and other workers. At the time it was thought that all matter could be accounted for but we now know that ths was a bit optimistic given the apparent need for dark matter and dark energy. However as the nature of the latter two forms of matter are somewhat elusive I think it's fair to say that the calculations of Peebles now collectively known as the Big Bang gives the best account we have of the calcluation of the abundance of the light elements and is a lasting achievement similar to the calculation of the energy levels of the hydrogen atom in quantum physics, the deduction of electromagnetic waves from Maxwell's equations and all the other key calculations of physics.

Whatever subsequent developments in Cosmology, it seems highly unlikely that this will be overthrown, Yes of course there are unknown questions at the edges but the big bang is here to stay. In this context the universe as far as cosmologists  are concerned is essentially that sea of neutrons, protons and their associated neutrino's which existed round about 1/100 th of a second to the first three minutes when the light elements were formed. A vague notion that the universe contains everything, the dreams and wishes of us all, our imagination and creativity as one of the correspondents wanted to claim is certainly not relevant to cosmology. Of course I'm not claiming that those issues are irrelevant, it's just that cosmology cannot explain those things it is just outside of cosmology's remit.

You might claim that by limiting the scope of Cosmology to the prediction of elemental abundances or developing models of Galaxy formation and all the other stuff of Astrophysics that this is not enough. Yet it is only by limiting itself to the prediction of measurable quantities that Cosmology and indeed physics as a whole gains it successes. By this means we can obtain the most precise account of what happened at the early stages of the universe that mankind has produced and that should be more than enough to satisfy most people.