You and your scare quotes.
Sorry, bad habits are hard to break. It took me forever to get rid of caps. I'm still working on limiting my use of terms for your non-demonstrated in the lab claims to less offensive terms like "supernatural".
Spacetime is the arena in which stuff exists.
But you just took all the stuff out! There is no arena in which stuff exists in your 'nothingness'. There's no geometric curvature. There's no "spacetime".
(and before you ask, no, it's not a physical arena made of girders or bricks, where they sell overpriced hotdogs).
Yes, GR describes an arena made of mass and energy, like your girders and bricks. You cannot remove the girders and bricks and still claim to have a stadium where you intend to see overpriced hotdogs.
The equations of GR can quite easily be applied to an empty arena. G = T.
It's entirely meaningless to do so. There's no curvature. There's no expansion of anything *substantive* inside that empty arena. There's nothing really to apply such theories to, and you have no evidence that the formulas have any meaning *in the absence of* all matter/energy. Nothing prevents you from applying Maxwell's equations to "nothing" either I suppose, but there's still no point to it.
If there's no matter or radiation, then there's no energy or pressure. So the T side of the equation is zero. You can still solve that equation, and some solutions have expanding space.
You've effectively tried to remove the entire basis of general relativity theory, namely mass/energy. Without it, you have no arena, you have no hot dogs to sell, you've got nothing to expand, nothing to contract, and nothing work with.
You still haven't defined "space" in any *physical* (not mathematical) way that doesn't turn "space" into a glorified aether.
Your objection is basically the same as taking F = ma and saying that if the total force is zero, then there can't be any objects moving. Obviously, that's wrong.
No, my objection is if m is zero, F can't be forcing space to accelerate off into the sunset.
Right, there are no objects in an empty universe. Nevertheless, the differential equations describe the changes in the metric.
Without any energy or matter to work with, you cannot demonstrate that any GR metrics even exist at all!
It is the metric that describes distances and intervals. If the metric changes, so do distances. Space expands.
The operative term in your statement was the term was 'if' the metric changes. You don't have a single atom or electron to your name, so you certainly cannot demonstrate in any controlled experiment that the metric changes and that space expands. The whole claim is a 'pure act of faith' on the part of the believer.
It's not that difficult. The stress-energy tensor has entries in it corresponding to the energy density and pressure. In an empty universe, there's no energy or pressure, so those entries are zero. Is that so complicated?
If there's no stuff in the universe...
...'mark it zero'...
Easy!
Marking it zero is fine. It's claiming that it still has curvature or it's still *doing* anything I'm not fine with. Nothing cannot expand. You've created a mystical nothing with mystical mathematical properties that have nothing to do with nothing, and everything to do with mass/energy.
Why would I acknowledge that? We know what the stress energy tensor looks like for charges. We know what the stress energy tensor looks like for electromagnetism. Be my guest. Plug them in. But it's not going to give you the negative pressure you need to make your EM universe static.
You still do not seem to appreciate that I do not 'need' the universe to be static, certainly not *completely* static in all places at all times. I'm fine with an 'expanding object' universe.
What you completely ignored was my discussion of what the Einstein tensor is made of (and thus, what GR is about). So let's sum it up again.
The Einstein tensor is made of the metric and the derivatives of the metric.
Gravity, the thing those mathematical symbols describe is a curvature of spacetime in GR theory, *caused by the presence of mass energy*. Without the *cause* the formulas apply to *nothing*, and *nothing* cannot do anything. Nothing cannot sing. Nothing cannot dance. Nothing cannot expand, and nothing cannot contract.
Thus, GR is a theory about how the metric changes.
GR theory is *not* about how the metric changes, it's about how mass/energy curves spacetime. The metric changes you're describing as dark energy and inflation are *absolutely not* necessary in GR, nor is GR theory dependent upon inflation or dark energy.
The metric is our rulers and clocks.
If the metric has nonzero derivatives, then our rulers and clocks are changing.
Bingo, space expansion.
You're still ignoring my EM field example, where the electric field does have a source and a sink, but the magnetic field does not. Time can change, but not the metrics. Furthermore the metric changes we observe are directly related to location and concentration of mass/energy, not the absence of it.
Again, you're not acknowledging that GR theory stands on it's own merits *without* inflation, and *without* dark energy. It's a complete theory without either claim and without the claim of an expanding metric.
Only one *otherwise falsified* cosmology theory requires all these "supernatural" claims that cannot be demonstrated in a lab.
