Dark energy and the Cosmological Constant

[Haelfix]

The cosmological constant business on the left hand side vs right hand side is quite silly to be honest. It's a complete triviality mathematically and there is no classical sense in which you can prefer one over the other, and in neither case are things any more or less mysterious with respect to the cosmological constant problem. (it is still 120 orders of magnitude too small on the left hand side if you want to think of it that way --curvature undergoes renormalization just like matter does when you promote the equations into the more fundamental quantum realm)

The only sense in which it might be important whether to group the term on the left vs the right is the ultimate prejudice about whether Einsteins equations holds through all energy scales. If for instance a modification occurs, then it is in fact important where you group things, b/c you may have a situation where physical quantities will differ.

 

[marcus]

Personally I find this physical interpretation of Lambda interesting (not one that is interchangeable with energy density however.)
The paper is only two pages so people who are interested in non-DE might want to take a look.
http://arxiv.org/abs/1105.1898

It goes back to some earlier papers by John Madore on the "fuzzy sphere". quantum uncertainty in measuring angle (as opposed to position, momentum...)

1. John Madore, “The Fuzzy sphere,” Class.Quant.Grav., 9, 69–88 (1992).
2. John Madore, “Gravity on fuzzy space-time,” (1997), dedicated to Walter Thirring on the occasion of his 70th birthday, arXiv:gr-qc/9709002 [gr-qc].
3. John Madore, An introduction to Noncommutative Differential Geometry and its Physical Applications., London Mathematical Society Lecture Note Series, Vol. 257 (Cambridge University Press, 2002).

 

[marcus]

Within a certain theoretical context all curvature can be converted back and forth with energy etc---and Lambda is simply a curvature interconvertible with an energy density, with no special physical meaning outside that context. Someone only familiar with that context may well think it is a mere formality how one treats the constant---doesn't make any difference which side, treat it as an energy density if you want, and so on.

But such a person might be interested in other research lines and open to giving them a hearing, because they are different from his or her own familiar context.
Another interpretation of the Lambda constant has to do with the compactness of the phase space of geometry. And the finiteness of the number of distinguishable states of geometry. This is not the phase space of a system particles moving in a fixed geometry but actually that of the geometry itself.
It is work that is just getting started, which gives what I think is a new physical meaning to Lambda. I'll get the link.
http://arxiv.org/abs/1502.00278
Compact phase space, cosmological constant, discrete time
Carlo Rovelli, Francesca Vidotto
(Submitted on 1 Feb 2015)
We study the quantization of geometry in the presence of a cosmological constant, using a discretization with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.
6 pages

Again it is a short paper, only 6 pages. So not terribly burdensome to read.

 

[PeterDonis]

Another interpretation of the Lambda constant has to do with the compactness of the phase space of geometry.

Yes, in the context of quantum gravity, as I understand it, having a nonzero $\Lambda$ turns out to make a big difference to the phase space of the theory. AFAIK, at the level of ordinary classical GR, this would require $\Lambda$ to be constant, not variable, so it would not exchange energy or momentum with anything else (which is consistent with our best current observations).

 

[marcus]

You put it concisely! In addition to this incipient compact phase space idea (which needs to be worked out in 4d) there are a bunch of papers by various people which explore incorporating Lambda in QG by replacing SU(2) with the quantum group version SU(2)_q. where q is a version of Lambda on the unit circle of the complex plane. Some authors:
Fairbairn and Meusburger
M. Han
S. Major
I should mention that the while the Lambda constant occurring on the LHS of the Einstein GR equation is a reciprocal area (and is formally interconvertible with energy density) what these authors are finding to be physically meaningful is the square root of Lambda, the reciprocal of a length constant. So in that work it is the square root of the Lambda we are used to, which is more fundamentally significant. that's what I should have said when I was talking about the quantum group q constant being a version of Lambda.

 

[Chronos]

This kinda reminds me of the shrinking universe idea. I still prefer the geometric interpretation - purely on the grounds of simplicity. Dark energy makes for a much more complicated universe, IMO.

 

[Buzz Bloom]

Perhaps someone interested in this thread would also be intereted in a posting I made earlier today inthe thread: "Why is the Universe (nearly) flat ?".
Reference https://www.physicsforums.com/threads/why-is-the-universe-nearly-flat.804427/

It involves an alternative to Lambda/Dark Energy which would also cause an acceleration of the Universe expansion.

 

[PeterDonis]

It involves an alternative to Lambda/Dark Energy which would also cause an acceleration of the Universe expansion.

See my replies in that thread.