# Accelerated Expansion from Negative Λ

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I think this is one of those papers that will have millions of citations

http://arxiv.org/abs/1205.3807

Accelerated Expansion from Negative Λ

James B. Hartle, S. W. Hawking, Thomas Hertog
(Submitted on 16 May 2012)
Wave functions specifying a quantum state of the universe must satisfy the constraints of general relativity, in particular the Wheeler-DeWitt equation (WDWE). We show for a wide class of models with non-zero cosmological constant that solutions of the WDWE exhibit a universal semiclassical asymptotic structure for large spatial volumes. A consequence of this asymptotic structure is that a wave function in a gravitational theory with a negative cosmological constant can predict an ensemble of asymptotically classical histories which expand with a positive effective cosmological constant. This raises the possibility that even fundamental theories with a negative cosmological constant can be consistent with our low-energy observations of a classical, accelerating universe. We illustrate this general framework with the specific example of the no-boundary wave function in its holographic form. The implications of these results for model building in string cosmology are discussed.

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bapowell
Yes. This might just be the adrenaline needle getting plunged into the heart of string theory.

marcus
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Dearly Missed
Yes. This might just be the adrenaline needle getting plunged into the heart of string theory.
Good image!

Thanks for posting this, MTd2. This summer at Strings 2012, Andrew Strominger is giving a talk about progress in dS/CFT correspondence. With this, that may not be necessary.

marcus
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Dearly Missed
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With this, that may not be necessary.
It seems there is a duality between AdS/CFT and dS/CFT. Maybe it is a huge advance in both fronts.

For those who do not wish to read the entire paper, here is an excerpt from the conclusion in the 'Summary' section:
Given this general framework, the argument proceeds as follows: The universal semiclassical asymptotic wave functions in theories with a negative cosmological constant describe two classes of real asymptotic histories - asymptotically Euclidean AdS for boundary metrics with one signature and Lorentzian de Sitter for metrics with the opposite signature. Assuming boundaries with spherical topology the classicality condition can be satisfied only for the asymtotically de Sitter histories. Therefore negative $\Lambda$ theories can be consistent with our observations of classical accelerated expansion.

Intrastellar
Gold Member
Interesting, to say the least ...
Thanks MTd2 for bringing this up

I think this is one of those papers that will have millions of citations

http://arxiv.org/abs/1205.3807

Accelerated Expansion from Negative Λ

James B. Hartle, S. W. Hawking, Thomas Hertog
(Submitted on 16 May 2012)
For somebody who has had a degenerative "terminal illness" for 40 years Hawking publishes a lot.

I may be able to convey something of how this paper works. It combines AdS/CFT with Hartle and Hawking's "no-boundary proposal" for the wavefunction of the universe.

First, visualize AdS/CFT as a solid standing cylinder and the no-boundary proposal as a solid sphere. The vertical direction in the cylinder is time, the solid interior is the AdS space, the surface of the cylinder is the CFT. The meaning of AdS/CFT is that quantum processes in the interior of the cylinder can be mapped to quantum processes taking place on the surface of the cylinder.

As for the no-boundary proposal, that is a way to obtain amplitudes for a state of the universe by summing over Euclidean histories which end in that state and which have no other boundaries. So in the solid sphere, the surface represents the end-state, and the interior represents a typical history contributing to the path integral. In theory, you could say that the time direction runs from the surface into the center, so the sphere consists of previous states of the universe in concentric shells, but in practice, you're in Euclidean signature, so you're using "histories" in which there is no real time direction.

I have described AdS/CFT in terms of a cylinder with time going up or along the cylinder, but you can do Euclidean AdS/CFT too. In that case, rather than a cylinder, you have a sphere, because both on the boundary and in the interior, you don't have space and time, you just have space.

So here we see a convergence. To calculate the amplitude for a particular state of the universe, you sum over Euclidean 4-geometries ending on a 3-sphere boundary with specified values of the metric and other fields. And Euclidean AdS/CFT involves an equivalence between such a sum, and a dual sum defined just on the 3-boundary, in CFT language.

So AdS/CFT offers a way to do the no-boundary calculation for cosmologies with a negative cosmological constant. But how do they get solutions with a positive cosmological constant? Basically, by complexifying the variables in the path integral - allowing e.g. the metric to take on complex values away from the final surface. So some quantities which classically were just real, can now be pure imaginary, and if you square them, you get a quantity which is real but of the opposite sign to what was classically possible. That's it, more or less, though the details are complicated.

Hundreds of AdS/CFT dual pairs have been identified, and certain conditions (described in the paper) have to be met if they are to be cosmologically relevant, so yes, this will certainly lead to yet another line of research in cosmology. In fact, six months ago I was rather excited about a particular AdS/CFT pair, because I found out that, just before the first superstring revolution, Murray Gell-Mann had tried to obtain the standard model from the AdS side (as a compactification of d=11 supergravity, which we now know as the low-energy limit of M-theory). Many years later, the CFT dual of that AdS theory was constructed, and I thought that if it could be uplifted to de Sitter space, we might get to describe the real world.

I'm not so excited about it now because I understand particle physics much better now, and Gell-Mann's construction has only an impressionistic resemblance to the standard model (though Hermann Nicolai, for one, remains intrigued by it). Nonetheless, I'm finding the details of the current paper (Hartle et al) so comprehensible, that I'll be tempted to go all the way, and at least see whether the "Gell-Mann model" meets the criteria for inflation and late-time acceleration, when evaluated via a holographic no-boundary wavefunction.

At the same time, I have major reservations about a lot of the formal manipulations that are carried out in quantum cosmology. Euclidean space, complexified metrics, no time evolution; if this truly is a description of reality, it needs some sort of radical ontological reinterpretation, e.g. as a twistorial Bohmian mechanics (I mention twistors because of the complex variables, and Bohm because the path integral is approximated by Hamilton-Jacobi trajectories).

Gold Member
Mitchel, it seems that the proposal is deeper than what you are saying. For example, that sphere is also identified with a de Sitter space. So, in the end you have a dS/CFT - AdS/CFT correspondence. That is extremely impressive because it seems dS seems to hard to deal with, though I don't know the detail of why is that. But one thing I am sure. The most general holographic model, that one from Bousso, always assumes a dS space as an asymptotic behavior of his model. So, in a way, this new paper is a concrete and direct realization of an holographic string theoretical model for cosmology.

A commenter at Lubos's blog found a sign error. Lubos thought it might invalidate the paper but wasn't sure and mailed Hartle. Version 2 of the paper was just submitted, Lubos and his reader are acknowledged, and the error is called a typo. So the paper stands. People need to start trying the idea on their favorite AdS/CFT dual pairs - N=4 YM, ABJM, Witten's moonshine dual for AdS3 pure gravity... I want to see it applied to the Vasiliev theory for which a dS/CFT extension of the duality was recently constructed, because then we have two approaches to dS for that theory, which can be compared.

Gold Member
I vaguely remember that Witten found that the moonshine dual for the black hole was wrong. Is this what happened?

member 11137
I may be able to convey something of how this paper works. It combines AdS/CFT with Hartle and Hawking's "no-boundary proposal" for the wavefunction of the universe. ...

At the same time, I have major reservations about a lot of the formal manipulations that are carried out in quantum cosmology. Euclidean space, complexified metrics, no time evolution; if this truly is a description of reality, it needs some sort of radical ontological reinterpretation, e.g. as a twistorial Bohmian mechanics (I mention twistors because of the complex variables, and Bohm because the path integral is approximated by Hamilton-Jacobi trajectories).
Certainly a pretentious affirmation for someone like me but I agree with the main idea developped in that paper. Furthermore it can be connected with a toy model giving the ontological reinterpretation you are looking for. Consider a small piece of vacuum-made tubular string extending under the double influence of polarizations tensions at the extremities and gravitation everywhere else. Then you get equations like (2.11) in the reference. Details can be read on my home page since 2009. My reservation is that that toy model actually applies to particles with imaginary (complex) energies.

haushofer