I understand all that. And it's all besides the point, because as you said yourself, the spatial part of the space is flat. So space is flat. That's it, prometheus. End of story. And all your outrage and abuse won't change it one bit.
So what? This space is at all times homogeneous. It's flat. There's no gravity in it.
Two other people that know what they're talking about have pointed out that just because the spatial sections of a metric are flat, the time direction is important and can cause a non zero curvature, as is the case in de Sitter (and AdS) space.
Physics depends on reality, not on how you write a metric.
I'm beginning to think you are a bot. I write
"rewrite the de Sitter metric," and you automatically chime in with
"Physics depends on reality, not on how you write a metric," despite the fact that, in the very same quoted text I say
"remember physics doesn't depend on what coordinates you use."
No I'm not. I don't know either.
What are you asking then?
You still don't get it do you? What I've been telling about homogeneous flat space is what Einstein said. I'm not making it up.
I've not read the source for your quote, but if Einstein did say that then he was wrong. Curvature and therefore gravity can certainly exist in homogeneous spaces as was shown by de Sitter and Friedmann, Robertson and Walker. The other alternative is that you simply misunderstood what Einstein was trying to say, as I believe I've suggested before.
No it isn't. Because WMAP has determined that space is flat, which means its homogeneous, and there is no gravity in homogeneous space. And let's face it, if the universe was constrained by gravity, how come it ever expanded?
This is not true, as AN pointed out. WMAP has shown that the universe is close to flat at this moment in time.
Ah, a well crafted and reasoned argument to counter what I said. Not. You should try. But of course you won't.
If you want a slightly less sarcastic version of what I said before then how about this: General relativity and what we know about the early universe from the CMB and other sources contradict your claim. The expansion of the universe is not like the time dilation of SR, but it's a physical "points in space getting further apart," effect. You say there was no yardstick to measure things in the early universe - it's not true either. There are at least 4 scales that I can think of off the top of my head that are known to effect the evolution of the early universe, and I'm not a cosmologist by any means. They are the Planck scale, the grand unification scale, the electroweak scale and the QCD scale.
And that analogy is the wrong one. A better analogy is a compressed elastic sphere. Remove whatever it was that kept it compressed, and it expands. All points in the interior of the sphere are moving apart from one another.
What exactly is the difference? The balloon has a force difference (the air pressure in the balloon vs. the tension) such that the balloon increases in size. Your example has some unspecified force difference where the elastic sphere (note; these are commonly called "balloons" in the public domain) also expands.
In any case, these are just analogies and whether they are good or not so good analogies is beside the point. We have GR to tell us exactly what is happening without the need for analogies.
I didn't suggest that the CMB did provide information about inflation.
Good.
You're reduced to abuse because you've been hoist by your own petard: the spatial part of the space is flat. It does you no credit, prometheus.
Saying you are wrong is hardly abuse. I can be a whole lot more abusive if you like.
LOL. Prometheus was talking about de Sitter space, not anti de Sitter space. And he said the spatial part of the space is flat. So that's it, egg on face, game over, Farsight wins again. Now face up to it. Einstein spoke of inhomogeneous space when describing a gravitational field, not an inhomogeneous space-time-manifold. Here it is again:
"This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)..."
The fact that you didn't recognise the distinction is your problem, not some deficiency of mine. Hence you can spare me the humpty-dumpty it means what I say it means squirming and the feather-spitting erudite outraged abuse. And don't back up stuff like this:
...where rewriting the metric makes the expansion of the universe go away. That's garbage and you know it. So don't lecture me about intellectual honesty.
I haven't got too much to add to what AN and JamesR have had to say about this except to say the following: $$g_{\mu \nu}$$ is a symmetric, rank 2 tensor. You can show that in d dimensions, while a generic rank 2 tensor has $$2^d$$ components, the fact that $$g_{\mu \nu}$$ is symmetric means it has $$\frac{1}{2}d (d+1)$$ components. That is where your
"...compelling us to describe its state by ten functions (the gravitation potentials gμν)" comes from - in 4 dimensions (ie,
including time) the metric tensor has 10 independent components. If Einstein was only talking about the 3 dimensions of space then he would have talked about the metric containing only 6 independent components.
Oops.
