To me this seems like a bit of a chicken egg problem.
Based on the redshift of light (plus the assumption that physics worked the same way back then and there as it does now and here), we can calculate by how much the space from source to us must have expanded over the duration that light was in transit. But we also need to either know at what point in time that light was emitted, OR how far away that object is in order to determine the actual expansion rate.
Conversely, we determine the distance of objects and 'age' of the light based on the observed redshift and the expansion rate of the universe (but to derive that we already need to know distance or age).
How exactly is this problem solved? Is there some non-linearity involved that allows to solve for only one possible expansion rate?
how can we know that physics worked the same way in the past and in other locations as it does now and here? For example, how do we know that then and there energy differential of electrons in transit (and thus emitted light wavelength) of chemical compounds was the same there and then as they are here and now? Or that c was the same, or that the Planck scale and the passage of time was/is the same?
Or maybe a bit more generally asked: What is the set of fundamental unmeasurable/unknowable a priori assumptions our current standard model of Big Bang cosmology stands on?
