Cerenkov said:
given the fact that the early universe was opaque and not open to visual investigation, how do we know anything about the universe's density during the first 380,000 years of its existence?
Because we have other ways of inferring what the properties of the universe were before it became transparent to radiation. For example, we measure the relative abundances of light elements in our present universe, and we apply our knowledge of nuclear reactions to infer what the density and temperature of the universe must have been to make those light elements. We know the density and temperature when the universe became transparent to radiation were way, way short of what's required for those nuclear reactions, so we infer that there must have been an earlier time when the density and temperature were much higher.
Of course that's just one line of reasoning. Overall, the answer is that we apply our knowledge of the laws of physics to back-calculate what must have happened before the universe became transparent to radiation. Those laws of physics include GR, meaning curved spacetime, and we have built a model of the universe's evolution in time, going back to the end of inflation, that makes use of those laws of physics and matches all the data we have. And that model tells us what the density and temperature were as a function of time.
Cerenkov said:
We neither 'know' nor 'observe' what the early universe was actually doing. Instead we extrapolate backwards in time using physical principles we know well.
Not just "physical principles"--physical
laws. As above, we have built a model using those laws. It's not just a vague extrapolation. It's much more than that.
Cerenkov said:
Theoretical models of the early universe make certain predictions and some of these have been confirmed through observation.
Yes. I gave an example above (abundances of the light elements).
Cerenkov said:
when scientists discuss the density of the early universe and its decrease through expansion, are they doing so solely on the basis of this kind of extrapolation?
They are doing it based on the model they have built using the laws of physics and the data we have. As above, it's not just a vague "extrapolation".
Cerenkov said:
given the lack of a boundary to yield a frame of reference for density
You don't need a boundary to have a meaningful density. Density is a local concept, not a global one. You can measure the density of air around you without having to know the total volume of the Earth's atmosphere, or whether it has a boundary.
Cerenkov said:
how do we know that the density at one time was different from that of an earlier time?
Because of the model we've built using the laws of physics and the data we have.
Cerenkov said:
In this thread the use of a coordinate system has been discussed as a way of measuring expansion.
No, as a way of
describing expansion. And it's not necessary, just convenient. There are invariants, independent of any coordinate system, that describe the expansion--I mentioned the expansion scalar in an earlier post.
Cerenkov said:
what about density, which changes as a function of the expansion of the universe? Is that how this works? That if the universe is deemed to be expanding, then density must also be deemed to be falling?
When you construct a model of an expanding universe using the laws of physics, yes, this is what you find.
