Gravitational Waves might explain some "dark matter" effects

I'll take a stab at it. Could be total rubbish but. :-)

I think they're implying that gravitational 'self' energy present in the form of gravitational waves produced early in the universe can affect expansion later on, in a manner that mimics dark energy. But they do point out at the end that while their calculations indicate a contribution in the correct sense - it is of some 14 orders of magnitude lower than what's observed.

The GR field equations are non-linear and as such are not generally solvable, so the theorists are all into approximations. Particularly the perturbative techniques where one assumes a base linear model and adds small variations which are represented by parameters. One then produces equations containing series of terms of progressively higher orders in those parameters. Thus a number less than one when squared becomes smaller, cubed even smaller again ... etc. You truncate the series to as few/many terms as you are game to manipulate and then crank the handle to get a prediction. So those variously named metrics refer to prior models from which they choose to spring forward from as a further/finer approximation.

'Back reaction' is a phrase that describes the loss of energy from something that radiates. So while an accelerating electron emits light it will be less energetic. Conservation of energy. I can't quite see what components of the early universe they think is doing the radiating, but in any case whatever has lost energy by such emission then evolves in the manner they describe. I think they're saying that the energy emitted as GW's returns later to accelerate the universe. But then I've never understood the whole 'negative pressure' thing. :-)

Now self energy is one way of expressing GR's non-linearity. As energy and mass are equivalent then any quantity of energy has mass and thus acts gravitationally. Specifically gravitational energy has such mass and so gravity can attract itself!

Take the Earth. If I have an Earth's worth of mass but spread out as a smear with each kilogram far from every other kilogram then that system won't have much gravitational energy of interaction - but it has potential as the lumps could fall together. Now if I assemble the Earth - bring all those kilograms closer to each other - then by convention this interaction energy of construction is nominated as negative, gravity being attractive. However this energy acts to produce a further gravitational effect. This is not the Newtonian energy in a potential well that we are used to. This is extra again, but is of far lower magnitude. I saw an estimate for this once, if you had to separate the Earth's mass back to infinite separation then ( amongst other things! ) you'd have to contribute a mass/energy equivalent of about a cubic kilometer of crustal rock to account for the energy of the field attracting itself. That's still a tiny fraction of the Earth's rest mass/energy, but WOW! :-)

Note that the factor of c^2 in E = m * c^2, and the relatively small value of G conspire to keep these higher order effects 'suppressed'. So while an enormous amount of energy gets released in an atomic bomb explosion, with the products being only slightly lighter than what you began with, that cuts the other way. So a large energy only converts to a teensy mass to act gravitationally or dynamically. A light globe is barely lighter for emitting it's light .... ;-)

As another example you may have wondered about is why the intensity of GW's emitted from some system falls off by an inverse law, and not as inverse square? If we're sending waves right out into spacetime which is basically flat far from the ruckus that caused them, then why don't they diminish in that distant region according to a flux spreading out over an expanding area type model? ( surface area of a sphere goes like the square of the radius and hence a diluted flux over that area goes like inverse square ). The answer is that the flux in effect reinforces itself, gravity pulls on gravity, and that acts to maintain the amplitude of the wave above what you'd expect without the self energy. If it wasn't for that then we'd really have no hope of picking up all but the closest of GW sources.

Anyhows what the authors are indicating is not a full solution, but that more complete attempts to solve the non-linear GR equations can predict the type of effects that could explain observations better. So one doesn't have to hypothecate new stuff like dark matter/energy, but just work harder with the GR theory we're already more certain about. Who knows what is the effect/magnitude of even higher order terms that are currently discarded during approximation? After all the mass of a proton is dominated by energy of interaction of the gluons - and that wasn't discovered until lattice QCD was played out fully by accounting for higher order terms.

The scalar/vector/tensor bit is referring to how one classifies these non-linear components of Einstein's GR equations. ( A tensor is a way of expressing how a factor along one direction/axis can influence what occurs along a different axis. So I could have a 'shear tensor' to describe the situation where I squash something in one direction causing the material to bulge in the plane perpendicular to that direction ).

Cheers, Mike.

I've just listened to a talk given by prof.Riccardo Giacconi on current trends in physics and astronomy. To summarize: he does not believe in strings theory, too far from experiments. The search for gravitational waves is very important. What is new in astronomy, aside from new telescopes both on Earth and in space, is the speed at which astronomers can communicate and share scientific results, that is the net. And we are a small part of this net.
Tullio

G'day Chipper! That's a neat article. Well written. :-)

What I found especially funny was, in the section on inertial/gravitational mass etc being derived from electromagnetic effects :

That would be the 'mainstream' mathematicians, aka 'physicists' who prefer not to be bothered by experiments. :-)

Another issue is that gravity isn't quantised, yet. You can't attribute energy to any particular part of the field, it just isn't localisable. One can take a gravitational wave, transform to some specific part of it in a valid way such that the energy of the wave locally disappears. You just 'freefall' ( not be subject to non-gravitational forces ) at the area of interest, and via the equivalence principle, your new local frame then becomes inertial and everybody just floats about lazily, unaccelerated and not getting energy from the wave. But the equivalence principle is a local rule only, so what's 'over there' is accelerating with respect to your frame. Observers 'over there' certainly appear to be pushed about by the wave, when viewed from here, that is they are absorbing energy from it to alter their motions. So you transform to 'over there', and the energy likewise vanishes when you arrive. To somewhere else ..... indeed to where you came from! :-)

This doesn't happen with electromagnetism, say. You can't ride the photon so to speak. You can't transform them away. It will always hit you going at the same speed c, it will have some frequency and thus energy to impart to you when you meet. It might be redshifted, but there are no zero frequency photons, and thus they all have energy.

So where are the gravitons? Are they around here, or are they 'over there'? Those people 'over there' are evidently getting shoved around by gravitons, so let's go 'over there' and see these gravitons .... stomp, shuffle, walk ..... whoops, they've disappeared. :-)

The key difference is what's called background (in)dependence. In GR it is the spacetime 'background' that is waving, in EM and other forces the fields and their quanta exist within spacetime.

Cheers, Mike.

Similarly so for time?

[joke alert] Is that not all a viewpoint of the relative connectedness and disconnectedness of the respective interconnectedness? :-p [/joke alert]

More seriously, how can we experiment to reveal something that is itself the experiment?... Just as how would entities inside a simulation be able to become aware that they are themselves just a part of the simulation? Unless that is, inconsistencies or flaws could be discovered and understood...

Keep searchin',
Martin

Err? Time is not quantised? Or the energy of the wave is not localisable in time? :-)

Ah, you have been watching Yes Minister ..... :-)

Well I suppose Matrix mechanics might help!:-)

Top question, and there's the rub. The uncertainties of quantum mechanics for instance are the result of not being able to get outside the system, so randomness is what we see. Probabilities are a way of quantifying the unknowns, and certainty only resides in the past.

Cheers, Mike.

( edit ) I now see the point of your first question. Does General Relativity gain you more beer in the bottle? :-) :-)

( edit ) To which the answer is, in a certain sense : No, but it might weigh more!

( edit ) I can see economic potential within the gravitational potential - "Come down to the Black Hole Beer Bar. We do not serve wimpy light ales!"