Could Anisotropic Expansion Explain the Dark Matter Effect?

[Edgar L Owen]

It seems to me a possible explanation of the dark matter effect could be as follows:

Thorne and Misner (p. 719 in Gravitation) note that the Hubble expansion is anisotropic. Empty space expands but the gravitationally bound space within galaxies doesn't expand.

This should obviously produce warps in the space in the boundary areas around galaxies.

We know that warps in space are gravitational fields. So this means that the uneven expansion of space should produce gravitational fields around galaxies where dark matter halos are thought to exist.

So why or why aren't such space warps around galaxies the source of the dark matter effect? If they aren't what are they?

This explanation would have the additional advantages of 1. being automatically dark since there are no particles involved, 2. Not depending on the existence of new particles beyond the Standard Model which aren't even known to exist.

Comments?

Edgar

 

[PeterDonis]

Thorne and Misner (p. 719 in Gravitation) note that the Hubble expansion is anisotropic. Empty space expands but the gravitationally bound space within galaxies doesn't expand.

No, that's not what they say. What they say is that the distance between galaxies expands, but the distances between parts of bound objects, for example the stars within galaxies, doesn't expand. Distances "expanding" (increasing with time) is not the same as "space expanding" (though the latter term is often used in pop science sources).

Also, your use of the word "anisotropic" here is incorrect (and MTW do not use that word--in fact they emphasize that in the model they are describing, the universe, on large scales, is homogeneous and isotropic). The distances between galaxies increase the same way in all directions. What you are describing here, if it were correct, would be a departure from homogeneity, not isotropy.

This should obviously produce warps in the space in the boundary areas around galaxies.

No, it doesn't. What MTW are talking about is a simple product of averaging, i.e., constructing a model of the universe based on averages over large distance scales, without even trying to model smaller scale departures from the average. They say so at the bottom of p. 719:

Only at this gigantic scale of averaging does the notion of homogeneity make sense

In other words, the model they are talking about is just an approximation over large distance scales, and does not capture the physics at smaller scales. To capture the physics at smaller scales, you have to use different models that cover, for example, a single galaxy and the space surrounding it out to some distance that is still less than the distance to the nearest other galaxies. In a model like that, there is no extra "warping of space" at any "boundary" between the galaxy and the space between galaxies.

Comments?

Your idea is based on a mistaken premise. See above.

 

[Edgar L Owen]

Peter,

Please explain how and why the expansion of the distance between galaxies is not equivalent to (the direct manifestation of) the Hubble expansion of space?

Sure, I understand the universe can be modeled as homogeneous at large scales, but we are talking about galactic scales here.

Thanks,
Edgar

 

[stoomart]

Please explain how and why the expansion of the distance between galaxies is not equivalent to (the direct manifestation of) the Hubble expansion of space?

Distances "expanding" (increasing with time) is not the same as "space expanding" (though the latter term is often used in pop science sources).

My understanding is this is a semantics issue. @PeterDonis recently gave a definition of "space" in another thread as:

a 3-dimensional spacelike slice of a 4-dimensional spacetime.

I'm a complete novice though so I'll let Peter give a learned answer.

 

[PeterDonis]

Please explain how and why the expansion of the distance between galaxies is not equivalent to (the direct manifestation of) the Hubble expansion of space?

The standard viewpoint of cosmology is that the expansion of the distances between galaxies defines what we mean by "expansion of space". But under that definition, "expansion of space" doesn't do what you claim it would do in the OP of this thread. So you must be using some other definition of "expansion of space", and it's up to you to show how the expansion of the distances between galaxies is equivalent to it.

we are talking about galactic scales here.

No, we aren't, because there is no "expansion of space" at galactic scales. At least, not under the standard definition (see above).

 

[Edgar L Owen]

Peter,

Either space is something that has a shape or it isn't. GR suggests that it does have a shape. If something that has shape expands unevenly that should produce distortions in the regions of the uneven expansions. And since GR tells us that distortions in space are equivalent to gravitational fields, the uneven expansions of space should produce gravitational fields.

Can you explain why this isn't correct?

Thanks,
Edgar

 

[PeterDonis]

Can you explain why this isn't correct?

It's hard to know where to begin. What textbooks or peer-reviewed papers about GR and cosmology have you studied? I'm guessing the answer is "not many", since you appear to have a number of fundamental misconceptions.

The only comment I can really make at this point is that your concept of what it means for space to "have a shape" does not appear to be correct. But since you are using vague ordinary language instead of precise math, I can't really tell for sure. Since this is an "I" level thread, you should be able to state your position using the actual math that is used in GR and cosmology. Can you do that?