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The only argument I've been able to come up with, is that the solutions that describe an expanding universe are what we get from Einstein's equation when we decide to look for solutions that describe a homogeneous and isotropic universe. Since our universe is both homogeneous and isotropic on large scales, we can expect one of those solutions to be a reasonably accurate model of the large-scale behavior of the universe, but we

*can't*expect it to be a good model of the small-scale behavior. So even though those solutions predict that e.g. a meter stick should expand (right?), which would make the expansion undetectable, it still shouldn't come as a huge surprise that meter sticks, solar systems and galaxies don't expand.

I haven't heard any better arguments from anyone else. Someone said that the reason why meter sticks don't expand is that EM forces are much stronger than gravitational forces. That sounds like an explanation that someone just pulled out of their you-know-what, but I don't know how to respond to that since I don't know that the real answer is.

I understand that on large scales space-time should look like a FRW space-time (is that the standard name for it?), and near a star it should look like a Schwarzschild space-time, but I can't see how those pieces fit together. Is it possible to draw some kind of picture that makes this easy to understand?

I'm looking forward to hearing your answers and learning something new.