# 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!

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## 6 thoughts on “Penrose in Pittsburgh”

1. wolfgang

So instead of ‘turtles all the way down’ it is ‘aeons all the way down’ ?
Does he actually suggest an infinite number of them?

2. Bryan

Yep! But at the same time, I don’t think his construction requires ‘aeons all the way down’ — you could just as easily paste together only two aeons.

A finite-aeon cosmology does seem more physically palatable. Unfortunately, I don’t think it would solve all the philosophical problems that Penrose is targeting: there would be no explanation of black-hole evaporation in the “latest” aeon, and no explanation of early-Universe low entropy in the “earliest” aeon.

3. yzue118

If the universe expand so much at the end of a given aeoan, so that it gets so cold to the point that even black hole is too hot and has to radiate all its mass outward. Then how is the universe supposed to get colder still to precipitate new matter once it pass through to a new aeoan?

4. Bryan

As I recall, it’s the “rescaling” across the conformal boundary that does the trick.

At the “end” of an aeon, the cold massive particles meet their demise. But the massless particles can be thought of as continuing to the conformal boundary at t=infinity — after all, massless particles don’t have proper time. So, an aeon ends with an initial spacelike conformal surface, with massless particles on it.

At the “beginning” of an aeon, as you get very close to the big bang, temperatures get so hot that all particles become massless. So again, you get a bunch of massless particles on a conformal surface.

Penrose’s trick is to identify these two conformal surfaces. But conformal surfaces (and, as far as we can tell, massless particles) are conformally invariant. So any notion of “scale” is lost as we cross the conformal boundary — what were cold, far-apart particles can become hot, close-together particles in a new aeon, depending on how the metrics of the individual-aeons are related.