Reddit mentions of General Relativity: An Introduction for Physicists

I'm not sure these are directly applicable, but these some thoughts popped in to my head after reading your post. I'm linking to pages outlining the relations I mention:

1. In rederiving the Friedmann Lemaître Robertson Walker metric, Hobson, Efstathiou and Lasenby draw on an analogy to Newtonian fluid flow in the energy-momentum tensor. Perhaps this approach can be used when considering other types of fluid flow?
   
   
2. Consider for a moment the case of gas. Velocity squared plays a part in the non-relativistic Maxwell-Boltzmann distribution. A relativistic generalization is the Maxwell–Jüttner distribution.
   
   
3. If the other two thoughts aren't applicable, perhaps Volume 10 of the Course of Theoretical Physics might help to answer your question?

If you want to understand the mathematics I would highly recommend General Relativity by Hobson et al.

It was our GR course text for 3rd year undergrad, and has a nice balance between physics and maths: as the title says it's specifically for physicists, so some of the tensor properties aren't derived completely rigorously. Nevertheless it's a thorough grounding in the maths of GR, and while focussing on GR it has several chapters on cosmological models and techniques.

So not one to buy but definitely a book to check out of the library if it's there.

> Are there any current experiments in the works that might give us a better idea of the nature of this stretching? I fully accept that people smarter than me have worked on this model, but I just don't see how that conclusion was made?

There's a lot of factors involved (like the cosmic microwave background etc https://en.wikipedia.org/wiki/Metric_expansion_of_space#Observational_evidence ) in how we arrive at the conclusion and if the above overview doesn't convince you it will be the best if you go to a library and get a book on cosmology and read through it. These are several 100 page thick tomes that summarize the science that has gone into this (including experimental, also including alternatives that have been checked and ruled out). Obviously there's a lot of details involved in this (which will be hard to fit into a reddit post) and you will have to look into this research in detail to judge it. Wikipedia gives an overview over the experimental evidence.

https://en.wikipedia.org/wiki/Metric_expansion_of_space#Observational_evidence

These are two good books that cover this.

https://www.amazon.com/General-Relativity-Introduction-Physicists-Hobson/dp/0521829518

https://www.amazon.com/Cosmology-Steven-Weinberg/dp/0198526822