Can Gravitational Waves Explain Uniform Space Expansion in the Universe?

[l0st]

I am looking at a couple of very interesting papers, published in MNRAS, that deduce, that the accelerated expansion of the Universe we observe can be attributed to gravitational waves, produced by a very distant merger of two or more universe-mass-scale black holes. The last one is on the arxiv.

In particular, as an amateur (CS background), I had doubts about their work due to a heated discussion arguing author's assumption, that GW do not gravitate themselves. However, recently I stumbled upon Peter Donis's Wave article here, that resolved some of my doubts.

Now one of the major questions for the authors young cosmological theory is how could they explain uniformity of space expansion. A common sense assumption would be that this expansion would only stretch space in the direction along the radii from the merger area. However, authors claim, that an observer freely floating above the event will experience uniform space expansion, rather than directional.

I was wondering if somebody experienced here has already seen that paper, and can clarify if the idea makes sense, and in particular, if gravitational waves from a single distance source can appear to stretch space uniformly as experienced by a freely floating observer.

 

[PeterDonis]

A common sense assumption would be that this expansion would only stretch space in the direction along the radii from the merger area.

Why do you think this is a common sense assumption?

 

[l0st]

Why do you think this is a common sense assumption?

That's a good question. And, thinking of it, it was incorrect. But I'd still see it as non-uniform.

The picture, that comes to mind is an expanding thick sphere. Seems obvious, that for an observer in that sphere, stretching along directions on the surface of the sphere will be uniform, however it is unclear why would stretching along the "depth" of it will be the same. What I am trying to say is that if it would be, than I rather see it as a coincidence, than a rule.

 

[PeterDonis]

The picture, that comes to mind is an expanding thick sphere.

Why?

 

[l0st]

Why?

How else would you describe a cosmology with a gargantuan black-hole(s) in the center with our visible universe freely falling to it, and getting stretched?

 

[PeterDonis]

I was wondering if somebody experienced here has already seen that paper, and can clarify if the idea makes sense

I hadn't seen it previously, but I am looking at it now. My initial reaction is that their derivation of a modified Friedmann equation looks fishy; basically they are taking the weak field approximation of the Schwarzschild metric, letting the two coefficients become functions of time and space, and then waving their hands and calling that a modified FRW metric. But this ignores some crucial differences between the two geometries.

I'll read through the whole paper before making more detailed comments.

 

[l0st]

I'll read through the whole paper before making more detailed comments.

Re-reading it now too.

 

[PeterDonis]

How else would you describe a cosmology with a gargantuan black-hole(s) in the center with our visible universe freely falling to it, and getting stretched?

I don't think that's what the intended cosmology is. There is a huge black hole at the edge of the visible universe, yes, but I don't think it's intended that we and the rest of our visible universe are freely falling towards it. We are expanding away from it. Otherwise their cosmology is obviously inconsistent with observation, since we observe ourselves to be expanding away from objects near the edge of our visible universe.

Also, if they really intend for there to be only one huge black hole, then their cosmology is obviously not homogeneous and isotropic, at least not from our vantage point. But we actually observe our universe to be highly homogeneous and isotropic from our vantage point, so again this cosmology would seem to be obviously inconsistent with observation.

I could make sense of their "huge black hole at the edge of the visible universe" description if they meant it as a heuristic--that is, they are doing the math for just one of these things, but actually they assume that such objects are evenly distributed all over our sky at roughly the distance of our cosmological horizon. That would maintain isotropy and at least some homoegeneity. But I need to read through the paper in more detail to see if that is really what they intend.

 

[PeterDonis]

The picture, that comes to mind is an expanding thick sphere.

How else would you describe a cosmology with a gargantuan black-hole(s) in the center with our visible universe freely falling to it, and getting stretched?

Apart from my previous comments, if we consider a standard black hole spacetime, while it's true that a small sphere of test particles will be stretched radially by tidal gravity as it falls (and compressed tangentially), there is no valid interpretation of this as "space expansion" that I'm aware of. So I'm not sure where you are getting that intuition from.

 

[l0st]

When I say freely falling, I mean lack (or negligible amount) of orbiting, or a non-gravitiation related force, that'd keep us afloat. Only in that sense. Sorry for confusion.

 

[PeterDonis]

When I say freely falling, I mean lack (or negligible amount) of orbiting, or a non-gravitiation related force, that'd keep us afloat. Only in that sense.

Ok, that clarifies things.

 

[l0st]

Also, if they really intend for there to be only one huge black hole, then their cosmology is obviously not homogeneous and isotropic, at least not from our vantage point.

I think they do claim that though, hence my question.

I could make sense of their "huge black hole at the edge of the visible universe" description if they meant it as a heuristic--that is, they are doing the math for just one of these things, but actually they assume that such objects are evenly distributed all over our sky at roughly the distance of our cosmological horizon. That would maintain isotropy and at least some homoegeneity. But I need to read through the paper in more detail to see if that is really what they intend.

Actually, I think, that the idea to compute considering only a single source makes some sense, as at least from what we see most of the matter is mostly affected by a single strong gravitational source with relatively rare exceptions for mergers. E.g. where we are, we can mostly ignore everything, but the Earth's gravity. For objects in solar system that would be Sun, etc.

 

[PeterDonis]

at least from what we see most of the matter is mostly affected by a single strong gravitational source

Not on the scale of the universe as a whole. On the scale of the universe as a whole the key driving factor appears to be the average distribution of matter on large scales. The "single strong gravitational source" approximation works well on much smaller scales, yes, but that's not what the model in the paper is trying to address.

 

[l0st]

Not on the scale of the universe as a whole. On the scale of the universe as a whole the key driving factor appears to be the average distribution of matter on large scales. The "single strong gravitational source" approximation works well on much smaller scales, yes, but that's not what the model in the paper is trying to address.

Its kind of interesting if the scale of the universe is the only exception, and it happens, that this theory removes this exception.

 

[PeterDonis]

Its kind of interesting if the scale of the universe is the only exception

It's not an exception. It's a consequence of the fact that modeling the universe as a whole is fundamentally different from modeling isolated systems within the universe.

To briefly expand on this in more technical language: our models of isolated systems are asymptotically flat, which means they are finite regions of matter surrounded by empty space out to infinity. The Schwarzschild geometry is such a model.

By contrast, our model of the universe as a whole has matter everywhere; there is no "infinity" where things become empty space. The FRW geometry is such a model. And such a model is fundamentally different from an asymptotically flat model. (This is one of the reasons I find the derivation of the modified FRW model in the paper fishy.)

The "scale" issue in the model of the universe as a whole is just a way of saying that the perfectly homogeneous FRW geometry is an idealization: of course the universe as a whole is not exactly homogeneous, but homogeneity is a good approximation on large enough scales, and that gives a good enough approximation to the exact dynamics of the universe as a whole. But dropping the homogeneity requirement does not change an FRW geometry into an isolated, asymptotically flat geometry like the Schwarzschild geometry; the two are still fundamentally different.

 

[l0st]

Universe could potentially have a fractal-like structure, rather than become homogeneous at some scale.

 

[PeterDonis]

Universe could potentially have a fractal-like structure, rather than become homogeneous at some scale.

But we don't observe that; we observe homogeneity on large enough scales. The strongest evidence for this is the CMBR: it is homogeneous and isotropic to about 1 part in 100,000. A fractal universe would not produce that kind of observation.