What is the matter in cosmology

[wolram]

This paper states that gravity gravitates, to me that is mind boggling, i can not even understand how these additive effects may alter cosmology.
arXiv:1509.06682
Let us start by recalling how interaction energies work in relativistic gravity. It is well known that gravity gravitates in Einstein’s theory, and one aspect of this statement is the fact that the gravitational potential energies between point-like masses in an asymptotically flat space are themselves a source of gravity 1 . T

 

[Drakkith]

It is well known that gravity gravitates in Einstein’s theory

It is? I swear I just read an insights article saying otherwise.

 

[Mordred]

I found the paper itself rather lacking on details.

 

[wolram]

I would have thought the solution would be found in two in falling black holes surly the merging rate would be logarithmic?
Anyway the question seems to pop up periodically and IMHO there should be some easy observable solution.

 

[wolram]

My unorthodox way of thinking is, that gravitational radiation is an osculation (in) space time and does not (carry) energy, that is if these osculations exist at all.

 

[Mordred]

I found reading Master geodesics rather informative on the hydrodynamic relations involved on the stress energy tensor relations.

http://www.google.ca/url?sa=t&source=web&cd=1&rct=j&q=master geodesics pdf&ved=0CBoQFjAAahUKEwj2qr7Gi43IAhUJNogKHY1BCEQ&url=http://www.physics.usyd.edu.au/~luke/research/masters-geodesics.pdf&usg=AFQjCNEfgdmtJcrbRynPVRh-hA-kWTD29g&sig2=tyIYwC7Nub-cO-RR-VVHXA

$$T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}$$

what I found lacking in the paper you posted is the related math. The author didn't show the FLRW metric or EFE

 

[wolram]

Without getting to abstract this paper arXiv:0901.4005v2 [astro-ph.CO] 6 May 2009, suggests that graviton graviton interaction exclude Dark matter and Dark energy.

Our present understanding of the universe requires the existence of dark matter and dark energy. We describe here a natural mechanism that could make exotic dark matter and possibly dark energy unnecessary. Graviton-graviton interactions increase the gravitational binding of matter. This increase, for large massive systems such as galaxies, may be large enough to make exotic dark matter superfluous. Within a weak field approximation we compute the effect on the rotation curves of galaxies and find the correct magnitude and distribution without need for arbitrary parameters or additional exotic particles. The Tully-Fisher relation also emerges naturally from this framework. The computations are further applied to galaxy clusters.

 

[Chalnoth]

My unorthodox way of thinking is, that gravitational radiation is an osculation (in) space time and does not (carry) energy, that is if these osculations exist at all.

Gravitational waves most definitely exist, and they carry energy. Otherwise the observed orbital decay of binary pulsars wouldn't be possible. But I'm not sure they contribute to the stress-energy tensor.

 

[Mordred]

Gravitational waves most definitely exist, and they carry energy. Otherwise the observed orbital decay of binary pulsars wouldn't be possible. But I'm not sure they contribute to the stress-energy tensor.

I wouldn't think they contribute to the stress tensor itself as far as the average stress tensor distribution, as its pulling energy from one region to another. I suppose it depends on the region being defined by the metric. Ie source of the wave or at the waves current location.

 

[timmdeeg]

I wouldn't think they contribute to the stress tensor itself as far as the average stress tensor distribution, as its pulling energy from one region to another. I suppose it depends on the region being defined by the metric. Ie source of the wave or at the waves current location.

If there is a local distortion of space-time with a certain frequency, shouldn't one assume a source of gravity to be responsible for that? I'm not sure at all, but would it make sense that there exists a source of gravity, which isn't a component of the SET?

 

[Mordred]

Yes the source of gravity is the same, but it's movement can induce changes via waves of the space time curvature.

What I tried to describe is the total stress energy due to the source doesn't change. However it's distribution changes.

 

[Chronos]

It gets pretty messy. not to mention confusing, trying to calculate the contribution of gravity to the stress energy tensor, as PeterDonis noted in his insight article. I think you would get something that looks like a perpetual motion machine in such a case. One of the fundamental axioms in physics is energy can neither be created or destroyed, merely transformed.

 

[Mordred]

I agree Chronos, Peterdonis thread has already given me insights I hadn't considered before. I await the third addition.

 

[grauitate]

This paper states that gravity gravitates, to me that is mind boggling, i can not even understand how these additive effects may alter cosmology.
arXiv:1509.06682

It is? I swear I just read an insights article saying otherwise.

Please a question for better understanding and to specify the term: What is meant by "gravity gravitates"?
Shall it mean the well known "Self Gravitational Interaction" ? (but at this Google gives only a very meagre result - here in addition I would suggest to shortcut it as "SGI") -
i.e. the gravitation of any mass (gaseous, liquid, solid) reacts back to the mass itself and then changes e.g. the density (e.g. H₂ clouds) or effects a collapse and in extreme changes the atomic and nuclear composition of that mass (e.g. neutron star) ? (of course always in dynamical equilibrium with the expanding forces) ?
Is it this, what is meant by "gravity gravitates" ?

So, generally and sloppy I would say: in a flat, expanding universe, SGI mainly acts only on the bodies itself: galaxies, interstellar gas & dust, stars, planets, but not on the universe itself.
In contrast to this, in a curved, not expanding universe, SGI additionally acts on the universe itself and e.g. defines its size and density and equilibrium temperature (i.a. principle of Mach)

 

[PeterDonis]

I swear I just read an insights article saying otherwise.

The article says that whether "gravity gravitates" depends on how you translate those words in ordinary language into a precise question stated in terms of well-defined theory. If you translate it one way, the answer is yes. If you translate it a different way, the answer is no. So the first thing to do before we can discuss whether "gravity gravitates" in any sense relevant to this thread, is to determine what translation we should use.

What is meant by "gravity gravitates"?

As above, there are at least two possible meanings for those words, one of which leads to the answer yes, the other of which leads to the answer no. The article (linked to above) has further details. The question is, which meaning do you think is relevant for this discussion?

 

[PeterDonis]

I wouldn't think they contribute to the stress tensor itself

They don't.

If there is a local distortion of space-time with a certain frequency, shouldn't one assume a source of gravity to be responsible for that?

Not a local source, no. Just as EM waves (distortions of electric and magnetic fields) can exist in vacuum, with no charge present locally, gravitational waves can exist in vacuum with no stress-energy present locally.

In both cases, there will be a source (charge for EM, stress-energy for gravity) somewhere in the spacetime. But it doesn't have to be in the same local region of spacetime as the waves are.

 

[timmdeeg]

Not a local source, no. Just as EM waves (distortions of electric and magnetic fields) can exist in vacuum, with no charge present locally, gravitational waves can exist in vacuum with no stress-energy present locally.

Ah, yes, if I remember correctly it is the Weyl tensor which doesn't vanish in this case, which is another story.

I have just read your article "Does Gravity Gravitate" wherein you have clarified the two answers. Now assuming many sources of gravity waves (like many stars produce EM waves) and viewing gravity "as a massless spin-two field", would gravity waves contribute a (negligible) positive value to the energy density of the universe then (like EM waves do)?

 

[PeterDonis]

I have just read your article "Does Gravity Gravitate" wherein you have clarified the two answers. Now assuming many sources of gravity waves (like many stars produce EM waves) and viewing gravity "as a massless spin-two field", would gravity waves contribute a (negligible) positive value to the energy density of the universe then (like EM waves do)?

There is a third post in the series (the second came out a few days ago) which goes into gravity waves. The short answer is, it depends. The usual interpretation of "the energy density of the universe" is the stress-energy tensor (more precisely, the 0-0 component of it in comoving coordinates). Gravitational waves do not contribute to that, for the same reason spacetime curvature does not; as discussed in the article, those things appear on the LHS of the EFE, in the Einstein tensor, not on the RHS, which is the stress-energy tensor.

However, gravitational waves do carry energy; they can do work on an object (heating it up, for example). The third post I referred to above discusses this. And it is possible to come up with an interpretation of "the energy density of the universe" that includes the energy carried by gravitational waves. (This energy density will, as you suspect, be negligible, as the density of EM waves is.) But on any such interpretation, this energy density is no longer a component of a tensor, which means you are giving up coordinate independence; your interpretation will only be valid in a particular set of coordinates, and you won't be able to express physical laws involving this energy density in a form which is invariant under coordinate transformations, the way you can with tensor equations in GR.

Also, on any such interpretation (that includes GW energy in the energy density of the universe), you are giving up conservation of the source (which I talk about in the Insights article); the thing you get by taking the ordinary stress-energy tensor and adding some expression for GW energy density will not have zero covariant divergence. So there is no way to have local energy conservation when GW energy density is included, the way you have it for the ordinary stress-energy tensor.

 

[timmdeeg]

Thanks for your detailed answer.

However, gravitational waves do carry energy; they can do work on an object (heating it up, for example). The third post I referred to above discusses this. And it is possible to come up with an interpretation of "the energy density of the universe" that includes the energy carried by gravitational waves. (This energy density will, as you suspect, be negligible, as the density of EM waves is.) But on any such interpretation, this energy density is no longer a component of a tensor, which means you are giving up coordinate independence; your interpretation will only be valid in a particular set of coordinates, and you won't be able to express physical laws involving this energy density in a form which is invariant under coordinate transformations, the way you can with tensor equations in GR.

Let'a assume a universe which contains binary black holes only, all of them close enough to merge. Once merged a lot of energy (GR-waves) was emitted while the mass of the black holes was decreasing accordingly.
I wonder how this scenario would influence the time dependence of the scale factor $a(t)$ and hence the dynamics of universe. It seems that the mass density will decrease. However as the energy due to GR-waves (being no component of the Stress Energy Tensor) does not contribute to the energy density (in the Friedmann equation) this energy should not influence $a(t)$ in the view of a commoving observer but eventually in the view of an observer "in a particular set of coordinates". Whereby I have no idea how regardinf such coordinates or such an observer resp.

Remembering various discussions in PF "true physics" is not coordinate dependent, e.g. increasing distances vs. stretching of space. Would you agree that in this sense the interpretation of energy density of GR-waves in your above post is not true physics?

 

[PeterDonis]

I wonder how this scenario would influence the time dependence of the scale factor $a(t)$

Heuristically, this would be transferring energy from ordinary matter to radiation, which would in principle affect the time dependence, yes. (In practice, the effect would probably be too small to observe, since the universe now is dark energy-dominated, not matter-dominated.)

as the energy due to GR-waves (being no component of the Stress Energy Tensor) does not contribute to the energy density (in the Friedmann equation)

Not directly, no. But transferring energy from ordinary matter to GWs will change the time dependence of the stress-energy tensor components in the Friedmann equation from what they would have been if no GWs had been generated. That will indirectly change the time dependence of $a(t)$.

this energy should not influence$a(t)$ in the view of a commoving observer but eventually in the view of an observer "in a particular set of coordinates".

As far as cosmology is concerned, "comoving" coordinates are the "particular set of coordinates".

Remembering various discussions in PF "true physics" is not coordinate dependent, e.g. increasing distances vs. stretching of space. Would you agree that in this sense the interpretation of energy density of GR-waves in your above post is not true physics?

No. The work done by gravitational waves on objects is invariant; it doesn't depend on your choice of coordinates. So the energy carried by GWs also doesn't depend on your choice of coordinates. (This is a heuristic way of saying it; strictly speaking, "work" and "energy" are not tensors but components of tensors, so they aren't invariant by themselves but covariant. But it's straightforward to construct actual scalar invariants corresponding to them for particular scenarios--things like work or energy applied to the system's invariant mass.)

 

[timmdeeg]

Not directly, no. But transferring energy from ordinary matter to GWs will change the time dependence of the stress-energy tensor components in the Friedmann equation from what they would have been if no GWs had been generated.

Which means that the matter density in the Friedmann equation decreases (in addition to the decrease due to expansion).

Thanks for your explanations and also for your insight articles, they are valuable for laypersons, who have problems to collect such information. I was just reading part 3.