How seriously do you take the FLRW model?

[skippy1729]

1. Isotropic? yes.

2. Homogeneous? Historically, the scale of homogeneity seems to be a moving target. As ever larger structures are observed, the scale of homogeneity is set just past the horizon, so to speak.

My real problem comes from the following thought experiment. Actually a pseudo thought experiment since it can not be performed.

Suppose the universe has a slight positive curvature. It is then closed and contains a finite amount of stuff. Now, by magic, we take one hydrogen atom from every cubic kilometer and make it disappear.
The curvature could now be exactly zero, or slightly negative. There are now two alternatives:

A. The universe could spontaneously transmute into an infinite flat or hyperbolic space containing an infinite amount of stuff.

B. The universe could spontaneously transmute into a flat toroidal or closed hyperbolic space, still with a finite amount of stuff.

My (scientifically unjustified) opinion of this pseudo experiment is that the universe should be finite. Perhaps I am just taking the model too seriously.

Cheers, Skippy

 

[sylas]

The curvature would be unchanged. I think it is the rate of expansion that would alter.

 

[marcus]

Skippy, I like your thought experiment.

... Now, by magic, we take one hydrogen atom from every cubic kilometer and make it disappear.
The curvature could now be exactly zero, or slightly negative. There are now two alternatives:
...

However I agree with Sylas.

The curvature would be unchanged. I think it is the rate of expansion that would alter.

Of course the thought experiment involves magic so it is somewhat unphysical. But to spell it out in more detail let's recall that the critical (energy) density is

rho_crit = 3 c^2 H^2/(8 pi G)

Now in your example you start with slight positive curved spatial closed universe (topologically a bumpy hypersphere)

say rho = 1.01 rho_crit = 3.03 c^2 H^2/(8 pi G) where H is the Hubble (expansion) rate, G is Newton, and c is c.

Now you reduce rho, say by 1 percent.

If H would stay the same, then you have a contradiction because now rho would equal rho_crit and she should be spatial flat infinite. That is your paradox. But maybe at the same time H decreases (by magic too). So that rho_crit reduces, say also by 1 percent. then you have the same old positive curved situation with your new density!

Again rho = 1.01 rho_crit and it is the same old hypersphere as before.

 

[skippy1729]

Thanks, I should have realized that magically changing rho would also magically change H, keeping everything (sort of) the same.

Skippy

 

[marcus]

Thanks, I should have realized that magically changing rho would also magically change H, keeping everything (sort of) the same.

Skippy

Heh heh. Well there is so much magic involved that it is hard to say how any of it could be physically implemented, so it is hard to say honestly what would actually happen. But I think it is an instructive question to ask, and hope you keep probing like that.

 

[sylas]

Read mainstream papers is my recommedation. Opinions do not cut it.

I don't think a mainstream paper will really deal with this thought experiment, which is pretty unphysical as phrased. But if you have a reference, that's fine.

Surely there is some value in trying to apply ones own knowledge of mainstream physics to toy examples. Otherwise why have a forum at all? We could all just sit back and read mainstream papers.

In my experience, I learn by reading and then applying -- and being corrected by others when I go wrong.

In this case, I suspect skippy is thinking in terms of simple equations like

$$\left(\frac{a}{\dot{a}}\right)^2 + \frac{kc^2}{a^2} - \frac{\Lambda c^2}{3} = \frac{8 \pi G}{3} \rho$$​

He's presumed that altering density (rho) would require an alteration to curvature. My point is simply that there's the $\dot{a}$ term he appears to have missed. Altering the energy density will alter the rate of expansion (and hence the rate of change of curvature), rather than altering curvature.

Cheers -- sylas

 

[Chalnoth]

Well, considering that such an alteration of the density would violate conservation of the stress-energy tensor, a law upon which the FLRW expansion is based, the result would be ambiguous.

 

[Chronos]

Apologies for the incomplete post. One of my favorite presentations is by Sean Carroll:
http://preposterousuniverse.com/writings/cosmologyprimer/index.html

 

[Hal King]

The inhabited parts of the universe are finite -- the rest can be anything you want it to be.

 

[Chalnoth]

The inhabited parts of the universe are finite

Why? How do you know?

the rest can be anything you want it to be.

I don't think reality cares what we want.

 

[Hal King]

I'm assuming we occupy a typical 'inhabited' part and we can only see a finite amount of universe.
(If we don't occupy an inhabited part, I'm not sure where that leads us.)

And 'reality' doesn't effect the unknowable. You can make up whatever you want with no fear of being proved wrong.

But I guess, this thread started by evoking 'magic' .. so anything is possible.

 

[Chalnoth]

I'm assuming we occupy a typical 'inhabited' part and we can only see a finite amount of universe.
(If we don't occupy an inhabited part, I'm not sure where that leads us.)

Well, perhaps if you meant that each individual inhabited part is finite, then you're okay. But it sounded like you meant that all inhabited parts in total are finite, which is by no means known.

And 'reality' doesn't effect the unknowable. You can make up whatever you want with no fear of being proved wrong.

But I guess, this thread started by evoking 'magic' .. so anything is possible.

Failure to be proven wrong doesn't mean you aren't. So it's better to ask what is likely to be correct, instead of what insane nonsense can I make up that can never be tested.

 

[Hal King]

I do agree with that ... but what does that mean for much cosmology today?

 

[Chalnoth]

I do agree with that ... but what does that mean for much cosmology today?

Nothing, because cosmology is an observation-driven science.

 

[Hal King]

Or better a science driven by what can't been seen ... dark matter, dark energy, ... ?

 

[Chalnoth]

Or better a science driven by what can't been seen ... dark matter, dark energy, ... ?

That is more than a little facile.

 

[Hal King]

Better than a 'rub goldberg' one.