The Value of the Cosmological Constant

[Chronos]

I found this new paper by John Barrow to be quite interesting:

http://arxiv.org/abs/1105.3105
The Value of the Cosmological Constant
Authors: John D. Barrow, Douglas J. Shaw
(Submitted on 16 May 2011)
Abstract: We make the cosmological constant, {\Lambda}, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and is the requirement that the cosmological wave function possesses a classical limit. When applied to the Friedmann metric it requires that the cosmological constant measured today, t_{U}, be {\Lambda} ~ t_{U}^(-2) ~ 10^(-122), as observed. This is the classical value of {\Lambda} that dominates the wave function of the universe. Our new field equation determines {\Lambda} in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature parameter of the universe is {\Omega}_{k0} \equiv -k/a_(0)^(2)H^2= -0.0055, which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological history.
Comments: 6 pages. This article received Third Prize in the 2011 Gravity Research Foundation Awards for Essays on Gravitation
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Extragalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th)

 

[TrickyDicky]

So is this positive spatial curvature of the universe compatible with inflation?

 

[Chronos]

Unsure if curvature is necessarily relevant to inflation.

 

[TrickyDicky]

Unsure if curvature is necessarily relevant to inflation.

I was under the impression that inflationist models had flat space as a requisite.

 

[yenchin]

I was under the impression that inflationist models had flat space as a requisite.

No. The point of inflation is that regardless of what curvature the universe started with, it then inflates so much that it appears very flat. After all, one of the motivation of inflation is to explain why the universe appears flat (flatness problem).

 

[yenchin]

I was under the impression that inflationist models had flat space as a requisite.

Oh I mis-undertood your point. Opps. But no, inflation doesn't necessarily means that the current universe must be exactly flat.

 

[yenchin]

In other words, the universe appears almost flat - we don't know if it is *exactly* flat. Perhaps it is born flat to start with due to some unknown physics, in which case inflation is not required to explain the flatness problem. But since we still don't know of such physical law, inflation was one of the proposal to explain why the universe appears so flat: in this scenario any curvature becomes inflated so as to become nearly flat. But note that if the space has curvature to start with, even after inflation, there is still curvature (although it is so so so much smaller than it was before inflation) since curvature scales as k/a^2 where a is the scale factor, which under inflation, goes like a(t)=exp(Ht). The universe inflates by 60 e-folds or so, and so k is divided by a large number. But in principle the curvature is still there and so should be detectable if you have very good detector or observation of some sort. The only way for the space to be *exactly* flat is that it was born *exactly* flat.

[Also take note that inflation is a good idea, but it is not necessarily true.]

 

[TrickyDicky]

Oh I mis-undertood your point. Opps. But no, inflation doesn't necessarily means that the current universe must be exactly flat.

I know, it means that the curvature if it exists must be very small and after checking the paper the curvature parameter of -0.0055 is consistent with the 95% CI from the data of WMAP on the curvature parameters.
But still, I think it makes a big difference to have k=0 or to have some curvature however small. If there is some curvature the spatial geometry changes from Euclidean to non-Euclidean and that may not be measurable locally but has consequences for the global shape of the universe. For instance, if the curvature is positive, it would make the universe spatially closed and finite (one could comeback to the same point after a finite time traveling in the same geodesic) and if negative, it would make it spatially open and either finite or infinite depending on the type of hyperbolic manifold.
OTOH I would say that only k=0 is in the spirit of the concordance LCDM model with inflation.

 

[TrickyDicky]

The only way for the space to be *exactly* flat is that it was born *exactly* flat.

Which would make inflation unnecessary to begin with.
So, I suppose you think the universe is spatially curved (however small that curvature is).

 

[yenchin]

Which would make inflation unnecessary to begin with.
So, I suppose you think the universe is spatially curved (however small that curvature is).

On the contrary I actually prefer an exactly flat universe for various reason (E.g. http://arxiv.org/abs/0711.1656). But that is just my personal preference (and bias)

 

[yenchin]

I know, it means that the curvature if it exists must be very small and after checking the paper the curvature parameter of -0.0055 is consistent with the 95% CI from the data of WMAP on the curvature parameters.
But still, I think it makes a big difference to have k=0 or to have some curvature however small. If there is some curvature the spatial geometry changes from Euclidean to non-Euclidean and that may not be measurable locally but has consequences for the global shape of the universe. For instance, if the curvature is positive, it would make the universe spatially closed and finite (one could comeback to the same point after a finite time traveling in the same geodesic) and if negative, it would make it spatially open and either finite or infinite depending on the type of hyperbolic manifold.
OTOH I would say that only k=0 is in the spirit of the concordance LCDM model with inflation.

True, but presumably if inflation occurs (and the subsequent expansion), the size of the universe may be so big now that circumnavigating it (to go around and come back) may no longer be possible.

 

[BillSaltLake]

I have a problem with the end of the paper ("" is Λ):
"There are other wider consequences of our scenario. At any given location and time, the
wave function of the universe is dominated by a classical history in which takes a single
constant value. Hence, no classical time-evolution of can be observed. Yet the history
that dominates, and its associated value, changes at different observation times. We see
a history with = 1, but an observer in our past would see a different history with =
2 > 1. For measurements of 1 and 2 to be compared, information would have to be sent from one history to another. At the level of classical physics this cannot be done. Observers will see a history consistent with the constant given by Eq.(2)[11]. Crucially, this includes registering all previous measurements of as being consistent with =1. Therefore, we do not see the past as an observer in the past would see it [12]."
We can certainly measure Λ now and "publish" it so that someone a billion years from now could see whether Λ_now > Λ_later. Remember that this theory requires that Λ be proportional to 1/t².
Anyway, the idea that Λ happens to be the inverse square of the Planck age is not new; neither is the idea that it's the cube of the Planck proton mass (now if they can paint a target around that arrow, at least Λ wouldn't be changing).

 

[oldman]

I'm surprised that Barrow's paper hasn't generated more discussion --- just a bit of quibbling about inflation.

I can't say I understand quite what the authors doing by "making" the Cosmological Constant into a field or, since they're not Zeus et al., rather supposing that it behaves like a field, and can therefore be involved in the action in a QED path-integral fashion.

And I can't grasp how and why this should let the constant's value be differently measured at different times by different observers, without being said to vary.

But this is probably my obtuseness. Their conclusions are startling:

Our simple extension of Einstein’s theory therefore has striking consequences: it explains the observed value of (Lambda), predicts the curvature parameter of the universe and paints a new picture of quantum cosmological history.

Is this possibly correct or is it being dismissed here as too startling to comment on? I'd like to find out.

 

[Chronos]

I found it rather startling myself, but, it does not appear plagued by dubious assumptions or mathematical sorcery. I think it is worth watching over the next year to see what Planck reveals.