Why all these prejudices against a constant? ("dark energy" is a fake probem)

marcus

==sample quote==
It is especially wrong to talk about a mysterious “substance” to denote dark energy. The expression “substance” is inappropriate and misleading. It is like saying that the centrifugal force that pushes out from a merry-go-round is the “effect of a mysterious substance”.
==endquote==

http://arxiv.org/abs/1002.3966
Why all these prejudices against a constant?
Eugenio Bianchi, Carlo Rovelli
9 pages, 4 figures
(Submitted on 21 Feb 2010)
"The expansion of the observed universe appears to be accelerating. A simple explanation of this phenomenon is provided by the non-vanishing of the cosmological constant in the Einstein equations. Arguments are commonly presented to the effect that this simple explanation is not viable or not sufficient, and therefore we are facing the 'great mystery' of the 'nature of a dark energy'. We argue that these arguments are unconvincing, or ill-founded."

marcus

The lambda constant is just a constant that naturally occurs when you write down the most general form of the action. With Einstein it was there already at the start! Not something he put in as an afterthought to make cosmology come out right.

==quote==
In fact, it is not even true that Einstein introduced the
λ term because of cosmology. He knew about this term
in the gravitational equations much earlier than his cos-
mological work. This can be deduced from a footnote
of his 1916 main work on general relativity [9] (the foot-
note is on page 180 of the English version). Einstein
derives the gravitational field equations from a list of
physical requirements. In the footnote, he notices that
the field equations he writes are not the most general pos-
sible ones, because there is another possible term, which
is in fact the cosmological term (the notation “λ” already
appears in this footnote).
The most general low-energy second order action for
the gravitational field, invariant under the relevant sym-
metry (diffeomorphisms) is...
...
which leads to (1). It depends on two constants, the
Newton constant G and the cosmological constant λ, and
there is no physical reason for discarding the second term...
==endquote==

tom.stoer

The cosmological constant becomes a mistery as soon as you do not write it on the left hand = "the gravity" side of the equations

[tex]R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}[/tex]

but it you write it on the right hand = "the matter" side.

[tex]R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = \frac{8\pi G}{c^4}T_{\mu\nu} - \Lambda g_{\mu\nu}[/tex]

In vacuum (with T=0) you still have some kind of "matter" which affects spacetime:

[tex]R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = - \Lambda g_{\mu\nu}[/tex]

If you leave this term on the left hand side, the question where it comes from and why it is there, is still open, but it is not a qustion about matter, dark energy or something like that; it is a question about gravity.

Finbar

lambda is the coupling to the volume of space-time. It belongs on the left-hand side you can see this from the fact that G does not couple to it. G couples to the energy-momentum.

The question is not why it is there but rather what sets its value. In particular why is it so small? One answer coming from the ERG approach is that there is an infra-red fixed point for which lambda=0. Hence on large scales lambda is small.

atyy

http://arxiv.org/abs/0910.5167 fig 3, 5 seem to suggest only a UV fixed point?

I think Xu and Horava http://arxiv.org/abs/1003.0009 got a IR fixed point, but not at z=1, which I think is what one would like?

BTW, has the evidence shifted away from AS now that CDT seems to have gone over to Horava? And does that mean that CDT is also problematic, since Horava seemed to have all sorts of problems.

Finbar

The IR fixed point is at the origin in fig 3. As you can see there is a trajectory that goes from the UV fixed point to the IR fixed point. But it would seem odd that we sit exactly on that trajectory.

I don't know what your on about with CDT, AS and Horava. CDT does not violate lorentz (at least not in the way Horava does). CDT uses the Regge action which which is a discrete version of einstein-hilbert. So i don't see why you think there is a connection between CDT and horava? If there is its not obvious.

marcus

Yes. Just like other constants, why is alpha = 1/137?
Why is the ratio of electron mass to planck mass so small?
I think part of the aim of the paper is to deflate some of the hype surrounding this particular constant.
Not to say it's not interesting though! It would be great to get some handle on why it's that particular size.

atyy

Is that really a fixed point? Also, if it is, is it's stability such that it would explain the cosmological constant (apparently not, since you say it's odd we'd be exactly on that trajectory)?

I'm thinking of - ?
http://arxiv.org/abs/0911.0401
http://arxiv.org/abs/1002.3298

Finbar

Hmm well both papers mention AS and horava. I think the CDT guys are hoping that it can be both AS and horava depending how they tune their parameters.


The gaussian fixed point is always going to be there as it just corresponds to the vanishing of the dimensionless couplings. But I don't think you need to be on a trajectory that flows to the IR fixed point. Better to read this paper

http://arXiv.org/abs/hep-th/0410119

"Assuming that Quantum Einstein Gravity (QEG) is the correct theory of gravity on all length scales we use analytical results from nonperturbative renormalization group (RG) equations as well as experimental input in order to characterize the special RG trajectory of QEG which is realized in Nature and to determine its parameters. On this trajectory, we identify a regime of scales where gravitational physics is well described by classical General Relativity. Strong renormalization effects occur at both larger and smaller momentum scales. The latter lead to a growth of Newton's constant at large distances. We argue that this effect becomes visible at the scale of galaxies and could provide a solution to the astrophysical missing mass problem which does not require any dark matter. We show that an extremely weak power law running of Newton's constant leads to flat galaxy rotation curves similar to those observed in Nature. Furthermore, a possible resolution of the cosmological constant problem is proposed by noting that all RG trajectories admitting a long classical regime automatically give rise to a small cosmological constant."

marcus

I'd like to get into the habit of thinking of it on the left hand side.
However I'm used to seeing the constant given in the form Omega_Lambda. A common estimate is Omega_Lambda = .73

That means the (fictional?) dark energy is 73% of critical density. If I express critical density in terms of today's Hubble rate H, then what I seem to get is that

Lambda = 3 *H^2* Omega_Lambda

= 3*0.73* (71 km/s per megaparsec)^2 ~ 10^-35 second^-2

Can you confirm that this is right way to get the lefthandside Lambda from the information we are usually given?

Naty1

Finbar posted:

I REALLY like that thought! What's the origin of these two relationships?? I don't mean I doubt it, but what led to these particular couplings?? Is it of purely mathematical origin or instead physical insights...or a combination??

"The man who had the courage to tell everybody that their ideas on space and time had to
be changed, then did not dare predicting an expanding universe, even if his jewel theory was saying so..." and " Even a total genius can be silly,
at times." .....suggests Einstein did not appreciate the nature of lambda early on.

tom.stoer

Yes, I can confirm that this is the way you get Omega_Lambda. But your interpretation
means that (implicitly) you think about it as something that appears on the right hand side: density, dark energy, ...

marcus

That's not what I was asking about. We are constantly being told that Omega_Lambda = 0.73, or thereabouts. We can take that as the current estimate.

What I never (or almost never) see an estimate for is LAMBDA ITSELF. The genuine lefthand side article.

That is what I want to calculate. I think it comes to 1.1 x 10^-35 second^-2
or thereabouts.

Would it be more correct to express it in units of reciprocal area, like in meter^-2?

That's what I think of as a common unit for curvature?

What I want confirmation for, or at least your opinion on, is if we are thinking just of the lefthandside form of the cosmo constant, which we are calling Lambda, and if we are given the commonly published figures of 71 for Hubble, and 0.73 for (fictional?) "dark energy fraction,"
then do we use the stated formula to get Lambda? Namely:

Lambda = 3 *H^2* Omega_Lambda

George Jones

Yes.

marcus

Good. Thank you George. So since I'm always seeing the published figures
71 km/s per megaparsec, and 0.73 (for the Hubble rate and the "darkenergy fraction") I can plug the blue thing into google and get Lambda.

3*0.73*(71 km/s per megaparsec)^2

Anybody can do it themselves. If you paste that blue expression into the google window, what you get is:
1.15946854e-35 s^-2

So that is what Lambda "really is", if you round off appropriately:

Lambda = 1.16 x 10^-35 seconds^-2
plus or minus whatever uncertainty is contributed by the 0.73 and the 71.

And you can change the numbers 71 and 0.73 to agree with whatever the latest observations indicate, and the google calculator will give you the corresponding estimate for Lambda, accordingly.

If Rovelli is right, and the others that share his views on the subject, then this is a basic constant of nature and we better start getting to know it, and getting used to it, and treating with some of the same respect we normally show basic constants.

atyy

Bianchi and Rovelli are not saying anything new, are they? Take eg. this 2007 review

http://arxiv.org/abs/0705.2533
"The observational and theoretical features described above suggests that one should consider cosmological constant as the most natural candidate for dark energy. Though it leads to well known problems, it is also the most economical [just one number] and simplest explanation for all the observations. Once we invoke the cosmological constant, classical gravity will be described by the three constants G, c and Lambda"

tom.stoer

I agree, they are not saying anything new. The stress the following
1) it is natural to consider Lambda as a constant of nature
2) one should distinguish between "QFT is the source of Lambda" and "QFT could cause corrections to the value of Lambda"
3) the reason for the puzzle is not Lambda, but Lambda on the right hand side of the equation ...
4) ... plus an idea how to calculate it - which fails by 120 orders of magnitude

Let's assume I have some biological theory; unfortunately it says not so much about about mammals, birds etc. but I claim that this theory provides an explanation of the zoogenesis of the duckbill from first principles. But applying this theory, it predicts the duckbill to look like an orca ...

Now I ask you: does this make the duckbill even more enigmatic, or does it mean that my theory is plainly wrong?