In article , Eric Flesch
writes:

Not much work seems to be done nowadays on open (aka hyperbolic) or
closed (aka spherical) manifolds,

What sort of work should be done?

Observations indicate that the universe is at least very close to
spatial flatness, which is probably why these models aren't mentioned
very much these days.

but it's instructive to consider
what they would look like as a nightsky. The answer is they would
look just the same as flat space, but if one were to hop in a rocket
and travel out there, one would find that objects are closer than
their angular size indicates in an open manifold (i.e.,
"foreshortened"), and in a closed manifold they would be further away
than expected.

Not just geometry but also expansion history determines the relation
between the angular and physical size of an object, for a given
redshift.

So nowadays we model that we can't visually distinguish at all between
these alternative curvatures.

The whole point of classical cosmology is to distinguish between such
models.

But spectroscopy illustrates how nature
finds ways to convey information -- astronomers of 100 years ago would
be astonished at how much signal there is in mere light. My
supposition is that there is indeed a visual way to distinguish
between open, flat, and closed manifolds, and that the cosmological
redshift shows us the way.

OK, classical cosmology also makes use of the redshift.

Regardless of all the complex constructs of standard cosmology, the
simple anchor is that cosmological redshift results from recession.
No recession, no big bang.

OK.

So alternative viewpoints of the redshift
are not welcome to some -- which is no reason not to try, of course.

You make it sound like the big bang is an assumption, but actually it is
a conclusion.

Lopez-Corredoira gave a useful review of static models in his paper
"Angular Size Test on the Expansion of the Universe" (2010
IJMP,19,245; arxiv:1002.0525) and observed (as have others) that 1/z
is well-fit to angular size across all redshifts -- without need of
evolution, dark matter, dark energy, whatever. Occam is calling.

The question is whether, within the observational errors, one can show
that 1/z is a better fit than, say, the current standard cosmological
model. Measuring angular size is easy. The hard part is determining
what physical size it corresponds to. This classical test has, due to
observational (not theoretical) difficulties not produced anything
useful up until now. (In some sense, CMB measurements are an
angular-size test, though.)

So these are threads for me to follow, hopefully to assemble into a
coherent whole, after the holidays. cheers, Eric.

We'll be looking for some testable predictions.