" you can also check how far from our location the host galaxy was when that GRB actually happened, if our best model is correct, of course."

You wrote "best model" more than once. How sure can we be that this model (the FLRW, I presume) is the best, or even remotely correct?

SL

Yes, I was referring to the generic FLRW model (or perhaps rather metric), more specifically, the Lambda-Cold-Dark-Matter (ΛCDM) model, a special case of FLRW.

It is easier to say why it is the 'best model' than to say it is the 'correct model'. Best in the sense that it fits our current observations better than available rival models. It is however sometimes called a 'toy model', because it is certainly not quite correct. For one thing, it ignores the lumpiness of matter (cold and dark) on smaller scales. Secondly, the mysteriousness of dark matter and dark energy is not all that comforting.

To create a general, inhomogeneous model that satisfies both observations and Einstein's field equations (EFEs) is extremely difficult - there are no exact solutions known for such a case. All one can do is to add inhomogeneity on to the ΛCDM to approximate the 'real thing'.

One such approximation is Wiltshire's TimesScape model, on which the 'jury is still out'. If it survives, TimeScape may do away with dark energy (or may at least reduce its significance). It automatically gives some apparent acceleration of the expansion rate, without dark energy. Dark matter is however still required in order to make it compatible with observations.

However, when Occam's razor is applied, the ΛCDM model is probably still the simplest solution that fits observations.

-J

"However, when Occam's razor is applied, the ΛCDM model is probably still the simplest solution that fits observations."

Yes, but doesn't that model only fit observations by tuning it until the results agree with observations. It does not give the value of any of the parameters from first principles, not so? It is not really a solution to the problem.

SL

The ΛCDM model is a solution to Einstein's Field Equations, which is derived from 'first principles'. We know from experiment that Einstein was right, or at least very, very close to right. Every testable prediction agrees with observation within experimental uncertainty.

At a cosmic level, those uncertainties are relatively large. What is 'tuned' are the values of the parameters inside the model, as you hinted. Cosmologists fit the parameters statistically to various models and then choose the model and corresponding parameter set that agree best with a fairly large range of observations. So far, the ΛCDM model has won.

-J