Penrose in Pittsburgh

Roger Penrose came to Pittsburgh on Friday, presenting his new picture of cosmology. It was my first time seeing a Penrose presentation, and I was delighted to find it filled with the same rich, beautiful diagrams that are in his books. Penrose calls his wild new proposal, "Conformal Cyclic Cosmology." Here's the basic idea.

Penrose proposes we construct a sequence of FLRW spacetimes (each one representing a model of cosmology in which the Universe is expanding), scale each one by a conformal factor, and then paste them all together to get a new spacetime. This new "super" spacetime is supposed to represent the Universe, as a sequence of expansion periods that Penrose calls aeons.

Now, in a bit more detail: Each FLRW spacetime is related to an aeon in the super-spacetime by a particular conformal transformation, which preserves causal structure, but which screws up length and time measurements. Under this transformation, both the big-bang and future-infinity become spacelike hypersurfaces, with finite time in between. So, Penrose proposes, the "big-bang" of one aeon can be identified with "future-infinity" in another aeon. This creates a sequence of aeons pasted together, each with the causal structure of an FLRW spacetime. The result is an account of the very large scale structure of spacetime, in terms of a nice general relativistic spacetime (no string theory, quantum gravity, etc.).

Woah. So, why on earth would you you that? Penrose thinks this model accounts for the three biggest problems in cosmology in one shot:

First: Explaining the apparent low-entropy state of the early Universe (Sean Carroll has recently attacked this problem. But the nice thing about Penrose is that he can actually give a precise statement of what it means for the early-Universe to have low entropy: it's called the Weyl Curvature Hypothesis (wikipedia). This hypothesis is true at the border between aeons in Penrose's Conformal-Cyclic-Cosmology -- indeed, this is apparently required in order to glue the aeons together smoothly. A remaining question, of course, is whether or not this is related in any useful way to the Boltzmann entropy on the scale of every-day objects...

Second: the black-hole information paradox. As I've ranted before: black hole evaporation isn't really a paradox, but rather a case where many physicists are demanding a more "complete" theory. Penrose is not one of them: he thinks information really is lost in a black-hole singularity. The Conformal-Cyclic-Cosmology model fits this view nicely. Very roughly, in order to smoothly glue together the aeons, it turns out that only conformally invariant matter fields can be around at the end of each aeon. So, black holes must disappear; the popping-out of "remnants" of particles when the black hole evaporates is incompatible with Penrose's model.

Third: the cosmic acceleration problem. This really is a problem. But Penrose says his model might account for it. Apparently, Penrose has calculated that some gravitational radiation will survive at the boundary between aeons in his model. He suggests that this could provide curvature to spacetime even in the absence of matter -- which is enough to generate an accelerated expansion.

This really is a wild proposal. But it's pretty surprising that such a simple model might deal with so many problems at once. Of course, there are not yet any good philosophical reasons to prefer this model over all the other proposals flying around in the zoo that is modern cosmology. However, Penrose did suggest one unique consequence of his cosmology, which is actually testable. Most cosmological models predict a perfect black-body spectrum in the Cosmic Microwave Background; Penrose is predicting a slight deviation.

In Penrose's Conformal Cycling Cosmology, a gravitational radiation field survives on the spacelike hypersurface representing the "big-bang" of our aeon. Moreover, that field is sensitive to conformal transformations, and gives rise to density fluctuations at the big bang. These fluctuations, according to Penrose, should manifest as ever-so-slight deviations in the CMB spectrum. He has suggested that conformally skewing the CMB might make these deviations more visible. Unfortunately, Penrose hasn't collected enough data to confirm or disconfirm his hypothesis. But it will be very interesting to see how this turns out!

Observationally Indistinguishable Dark-Energy Theories

Fundamentally different theories of dark energy may be underdetermined by observation, according to a recent preprint by Sanil Unnikrishnan.

Background. Dark energy was first proposed as a solution to the problem of cosmic acceleration. That is, if you propose the existence of an exotic form of matter (generically labeled "dark energy"), you can account for the observed FRW-expansion, as well as for the late-time ISW effect. However, there is now a whole zoo of different ideas about what dark energy is and what it's like: quintessence, k-essence, "phantom" energy, or even tachyons -- objects travelling at super-luminal speeds. (Here's a nice review of some of the options, by Sean Carroll.)

The Result. Whatever the nature of dark energy, the only observational access we currently have to it is through its effect on cosmic acceleration. This effect is determined by (global) parameters: the ratio of pressure to density of dark energy, and the ratio of pressure-fluctuations to density-fluctuations.

But what if there were two distinct models of dark energy that gave the same values for these parameters? Then those two models would be indistinguishable by observation. This is the situation that Unnikrishnan argues that we are in. In short: suppose dark energy is modeled as a scalar field (as it is in most of the above proposals). Then any values for these two parameters that you might measure can be derived from distinct scalar field Lagrangians -- different models of dark energy.

Some Implications. This would appear to lead to an epistemological quandary. Dark energy is being proposed as a fundamental feature of our universe. So it would be very fishy indeed if the fundamental nature of dark energy were in principle unknowable.

However, the underdetermination isn't quite as bad as that. If dark energy is what the physics community ends up accepting, then it's unlikely that our current observational access to dark energy is all we'll ever get. For example, if we ever succeeded in making any kind of local observation of dark energy in the lab or solar system, then we'd have new dark energy parameters to measure, which would not be underdetermined by this trick.

Furthermore, there are plenty of excuses for cosmic acceleration that don't model dark energy as a scalar field -- for example, those in which a cosmological constant is added to the field equations, and those which model it as the result of early-universe inhomogeneities.

Still, one can't help but feel a bit uneasy about the whole dark energy program. Historically, it looks a bit too much like Descartes' vortices -- and results like this one don't make us feel any better.

Is the cosmological metric about to flip Euclidean?

The 'wildest excuse for cosmic acceleration' prize so far should go, in my view, to these guys. They argue that the metric form of spacetime is about to flip from (-+++) to (++++), which they say produces the appearance of an accelerated expansion. Here's a little background on why they're suggesting this.

Cosmic Acceleration: a very brief background. Around 1998, the majority of physicists accepted that expansion of the Universe is accelerating. Since then, all bets are off as to the large scale structure of the spacetime. The experts simply don't agree as to what kind of Universe we live in, and it sometimes seems that the wilder the proposal, the better. This makes peering over the fence at the zoo of cosmological theories rather entertaining.

There are a lot of competing theories out there -- that exotic matter causing negative vacuum pressure is spread throughout spacetime (this is the "dark energy" that you hear so much hype about), that backreactions due to the inhomogeneities of the early Universe gave the expansion an extra kick, or that the speed of light is not equal to c on cosmic scales (so that we're not interpreting our data correctly).

But a changing metric signature? As it turns out, this idea isn't totally unheard of; as of today there seem to be around 50 papers on arXiv dealing with models of quantum gravity in which the signature of spacetime changes. It just wasn't clear until recently that this could be used to account for anything to do with the accelerated expansion.

(Wait a minute -- so why didn't a treatment of changing signature appear in my general relativity textbook? Well, the metric signature doesn't change in traditional general relativity. Most derivations of the Einstein Field Equations assume non-degeneracy of the metric, which is sufficient to fix the metric form for all of time. So the approach to cosmic acceleration here falls under the category of -- *gasp* -- changing the field equations.)