Yeah, this is point 2., what does "expansion of space" mean?
Other people may disagree but I think it is kind of meaningless if you are just talking about General Relativitythe very general theory of all kinds of spacetime geometries (or spacetimeandmatter, to be more inclusive)
In a very general context it would be kind of academic, and in some contexts not even too meaningful, to talk about "expansion of space."
But there is a separate forum called Relativity forum to talk in general terms about Relativity and that is not what this Cosmology forum is about.
here we are talking about the special case which is OUR universe.
For instance our universe has the Cosmic Microwave Background with a certain observed temperature essentially the same in all directions. (if you adjust a fraction of a percent for the solarsystem's motion)
that is a very special thing about OUR universe that makes it different from the general situation you get in more theoretical relativityit is far from the only important special feature! But it is an obvious example to make the point.
the CMB immediately defines what it means for an object to be STATIONARY in our universeit gives us an idea of rest called being "at rest with respect to the Hubble flow". there are actually two different definitions which give the same idea of stationary, coming at it from different directions. The Hubble flow is the recession of distant galaxies, essentially the same in all directions if you adjust for solar system motion.
this is a place where practical mainstream Cosmology departs from the mathematics subject of pure General Relativityin pure relativity (special or general) you don't have a CMB and you don't necessarily have a Hubble flow, and you don't get handed a universal idea of rest.
but in Cosmology, which studies our universe, you do get those handy extra features.
have to go. I'll get back to this when I have some more time. :)
