## Saturday, November 27, 2010 ... /////

### Penrose's CCC cosmology is either inflation or gibberish

Concentric circles, if real (which is unlikely), may come from cosmic strings or domain walls that were "exploding" during inflation

What Penrose and Guzardyan have rediscovered is the L=40 bump in the WMAP data
Vahe Gurzadyan of Yerevan and Roger Penrose of Oxford have submitted an ambitious preprint,
Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity (arXiv).
Echo chamber: BBC, UPI, Science News, Phys Org, Pop Sci, IO9.com, Physics World, Phil Gibbs
The authors claim that some concentric circles observed in the WMAP 7-year data at the 6-sigma confidence level provide us with evidence supporting Penrose's idiosyncratic version of pre-Big-Bang cosmology. (Their arithmetics clearly has to be checked by a serious person because 6-sigma corresponds to the 2 x 10^{-9} probability rather than 10^{-7} as they state.)

For a couple of years, Penrose has been saying that there was a period of cyclic events when the Universe was much smaller than it is today. The model is called Conformal Cyclic Cosmology (CCC).

Well, the word "model" is exaggerated. Instead of equations or any quantitative definition of what was happening before the Big Bang according to Roger Penrose, you have to live with Roger Penrose's smile and vague handwaving.

Causal diagrams

There exists one important tool to determine the possible causal relationships between any pair of events in any curved spacetime. When we talk about the newest inventions by Roger Penrose, it must sound as a complete coincidence that the tool is called the Penrose diagram. It's a picture depicting a 1+1-dimensional geometry that differs from a particular 1+1-dimensional curved spacetime by a local Weyl rescaling (metric(x,t) goes to metric(x,t) times const(x,t)).

This simple rescaling doesn't modify the two-dimensional "angles" - well, more precisely, rapidities because we are talking about the geometries of the Minkowski signature. Consequently, the light-like lines may still be identified with all the lines whose slope is 45°. In this form, the Penrose diagrams are directly relevant for 1+1-dimensional geometries as well as higher-dimensional geometries with a rotational or symmetry powerful enough to describe the equivalence classes (orbits) of points in spacetime by 2 coordinates.

What is the Penrose diagram of the Big Bang?

Here it is. But you must erase everything below the horizontal "Big Bang" line. The Big Bang event at "t=0" is represented by a horizontal, i.e. space-like, boundary of the spacetime in this diagram. That's why there can't be anything before the Big Bang. What you see at "t=0" is the initial space-like singularity of the Universe.

This beginning of the Universe has serious consequences. Two events at "t=0" with different values of "x" couldn't have shared a common past. That's why it's hard imagine how they communicated about their need to have the same temperature - which is what we observe in the cosmic microwave background.

This so-called horizon problem was identified in the 1970s as an awkward feature of the Standard Model cosmology. It is not a straight inconsistency but it does suggest that the underlying theory needed some particular fine-tuning of the initial conditions to agree with the observed properties of the Universe, especially the nearly constant temperature of the microwave background across the skies.

In this sense, the horizon problem is analogous to the hierarchy problem in particle physics. They're not inconsistencies but they're proofs of some arrangements that should have an explanation but the existing theories don't explain them.

Completely off-topic: "Horehronie" (Countryside around upper Hron river) by Kristina was the 2010 Slovakia's representative in Eurovision and remains a hit both in Slovakia and Czechia

The horizon problem, together with the flatness problem and other problems, was solved by the inflationary cosmology in 1981. Alan Guth was playing with the Higgs fields in cosmology when he discovered their ability to do something that turned out to be far more important than his original motivation. The Higgs fields optimized for the new job were renamed as inflatons. Their potential was improved and flattened a little bit.

These scalar fields may sit near the maximum of their potential for quite some time. While they're doing so, the Universe is expanding exponentially - much like the current Universe is expanding due to the cosmological constant. However, the temporary cosmological constant coming from the inflaton field - which was driving the inflationary expansion - was greater by dozens of orders of magnitude than the current cosmological constant.

What happens with the Penrose diagram? Well,

the horizontal line that used to be the boundary of the spacetime is no longer a boundary. The Penrose diagram gets hugely expanded into what would be previously called negative values of "t". It doesn't become infinitely long but it becomes long enough; the length of the Penrose diagram is given by the number of e-folding in inflation. The events at "t=0" with different values of "x" do share a common past. Inflation explains why different directions in the skies can have the same temperature of the microwave background.

It also explains why the spatial section of the Universe is so accurately flat and why the size and the mass of the Universe are so much bigger than the Planck length and the Planck mass. Everything boils down to the exponentials arising from the exponential de-Sitter-like expansion in the inflationary era.

Conformal Cyclic Cosmology

Now, inflation obviously solves the problems it claims to solve and whoever claims it doesn't simply doesn't understand physics too well. By completely irrational arguments (that also included crazy Carroll-like nonsense about the arrow of time), Penrose has been criticizing inflation for decades. Did he propose his own picture to extend the Big Bang theory?

Well, his recent creation is called the conformal cyclic cosmology (CCC). It also extends the Penrose diagram to the eon before the Big Bang. However, Penrose won't tell you what the actual proper distances are in the new portions of his spacetime. If he had done so, he would be forced to admit that the geometry is identical to inflation - exponentially growing proper distances: it is the only conceivable solution.

Instead, he only tells you what the conformal structure of the spacetime - and the Weyl tensor, the part of the Riemann tensor that only depends on the conformal structure (i.e. that is invariant under the Weyl rescalings) - is. Is that enough?

Well, it would be enough if he had a theory whose Lagrangian - or other basic equations - don't depend on the metric but only depend on the conformal structure (the metric modulo its scaling at each spacetime point). However, as you may guess, he doesn't have anything like that.

In most physical theories, the whole metric tensor - and not just the conformal structure - is essential to construct realistic actions which are essential to describe physics of the systems we know. You need the metric tensor to provide you with the upper indices to contract the lower indices from the derivatives in the Lagrangian. You need it for other things, too. Proper distances are physical.

While the electromagnetic field is classically scale-invariant, massive fields are clearly not: they have privileged proper distance scales. For example, the electron field is associated with the Compton wavelength of the electron. This is true for any other scale in particle physics. Even more universally, the Einstein-Hilbert action itself - the Lagrangian of general relativity - depends on the metric and not just the Weyl tensor.

It seems almost guaranteed that this dependence is not just an artifact of an approximation. Holography shows that the information that can be concentrated into a volume is bounded by the proper surface of this volume in the Planck units. The proper distances (and areas) matter.

In the context of CCC, you have two options: you either insist on the existence of the metric tensor, including the scaling, at each point. Then you are obviously led to the inflationary geometry as the right and natural answer: Penrose would "rediscover" inflation. (Of course, it wouldn't be quite an independent "rediscovery".)

Or you say that the overall scaling of the metric is ill-defined. Then you don't have to conclude that you deal with inflation. However, you also don't have any theory that could continuously connect to the theories we know - the Standard Model and General Relativity - in which the proper distances and scales are clearly real and important. Penrose is clearly trying to obscure this fundamental point but he simply doesn't have a single glimpse of such a theory.

Inflation could predict concentric circles

Let us look at the simple picture again:

The way how the pre-Big-Bang evolution could imply the existence of concentric circles is totally obvious: there is a world line of an object that is doing something periodic in the pre-Big-Bang eon (before what used to be called "t=0"). The outgoing future light cones of these periodic events are imprinted into the microwave background and displayed as concentric circles. This explanation is so obvious that I won't waste more time with it.

However, you see that as far as the causal structure goes, inflation is just perfect to explain such concentric circles. Gurzadyan and Penrose repeat about 10 times that the CCC is not inflation and there's no inflation in their model and that inflation couldn't explain the data. Nevertheless, they fail to mention that their model is either isomorphic to inflation or it is gibberish, and because of the identical causal structure, inflation has exactly as much capacity to explain the data as the CCC.

Well, indeed, the badly needed correction to their statements would sound as one of the Radio Yerevan jokes that Mr Gurzadyan of Yerevan must know very well. ;-)

Whether a particular inflationary model can give quantitatively satisfying predictions for such concentric circles requires a more accurate analysis. However, it is likely that the Gurzadyan-Penrose argument that inflation couldn't predict such concentric circles is incorrect. First, they correctly state that for inflation to predict such concentric circles, the source of the oscillations would have to occur many e-foldings before the end of the inflation.

Most non-uniformities that occur many e-foldings before the end of the inflation are indeed supposed to be flattened out and diluted. Perturbations of various fields decrease as powers of the size of the Universe. However, the exponents depend on the dimensions of the fields and other things.

The most general objects with the most general parameters embedded in inflation give the very same results as CCC - while the latter is incalculable. Gurzadyan and Penrose don't discuss the intensity of the concentric circles that the CCC predicts. If they had done so, it would be damn obvious that the problem is pretty much equivalent to the problem in inflation. Most likely, they would also get a brutal dilution out of the simplest models. But they are hiding behind the absence of any quantitative equations of the CCC, imposing the unjustified wishful thinking on their readers that the CCC can offer a better solution than inflation.

Extended cosmic objects may have the required longevity

I do agree that a simple enough inflation-like picture would probably tend to weaken the circles too much after many e-foldings. However, there could be explosions within inflation that could avoid the decay. The equation of state for the matter created in such explosions could have a negative pressure which would prevent it from decaying.

Recall the text Why and how energy is not conserved in cosmology to realize that the total mass stored in the dust is conserved and the total mass stored in positive-pressure types of matter such as radiation is decreasing as the Universe expands.

On the other hand, the total mass stored in negative-pressure forms of matter is increasing. The energy carried by the cosmological constant is an extreme example. But cosmic strings and cosmic domain walls have a negative pressure, too. So the total energy/mass carried by these objects is increasing as the Universe grows.

For the readers who care about the quantitative issues, strings have the stress energy tensor of the type "(+1,-1,0,0)rho" where the directions are time, space along the string, and transverse spatial directions. That's because the stress-energy tensor within the worldvolume is proportional to the metric tensor for the world sheet to preserve the internal Lorentz symmetry. No momentum components are flowing away from the world sheet so the transverse components vanish. By averaging over the directions in the 3D space, you get "(+1,-1/3,-1/3,-1/3)rho" for the cosmic strings, giving you "p=-rho/3". In the same way, membranes have "(+1,-1,-1,0)rho" or "p=-2.rho/3" after the isotropic averaging.

If you create an exploding cosmic string or a domain wall during the inflation and these objects are getting bigger, the total energy carried by these objects will increase with time and the local strength of the effect may stay pretty high.

At any rate, if Penrose and his collaborator preferred proper physics solutions of problems over tendentious non-quantitative bullshiting with the predetermined (and unjustified) goal to attack inflation, they would realize - like your humble correspondent - that the fact that the circles don't get too "weak" simply means that what is propagating is associated with objects with negative pressure such as cosmic strings and domain walls.

And that's the memo.

P.S.: I haven't made it sufficiently clear but I doubt that a new effect of the type they describe is really there in the data. One has to do a pretty sophisticated calculation to see whether some structures may appear as "chance". In particular, the WMAP data may be decomposed to the spherical harmonics labeled by "L,M" which depend on "L" in a well-known way.

This structure of the WMAP acoustic peaks, especially the largest first one, means that the temperature variations in 2 pieces of the skies are much more likely to be correlated if the points are separated by 1 degree than 2 degrees or 0.5 degrees.

Penrose et al. could have just seen the statistical signs of some "acoustic peaks" as a function of "L" - and "acoustic peaks" are well explained by the standard cosmological evolution. In my opinion, Penrose doesn't really understand these technical things about the Big Bang cosmology so he can't reliably determine whether he has discovered a "new effect".

Update: Penrose may see L=40 peak

I have thought about the acoustic peaks a bit more quantitatively and I think I know exactly what Penrose et al. see: they see concentric circles whose radii have periodicity 5° on the sky; see their paper. If you look at the graph above, you will see that 5° corresponds to L=40. And indeed, there is a small observed WMAP peak around L=40. The L=40 WMAP black datapoint is significantly above the red predicted curve, much like the L=22 peak is significantly below the red curve.

The "excessive" spherical harmonics with L=40 and low values of M will manifest themselves as concentric circles whose apparent (angular) radii differ by multiples of 5°. I don't know why there is exactly the deviation for L=40 but the graph above brings the effect to the perspective. It's just a tiny bump on a much stronger and more structured curve that is reproduced by the WMAP data and whose bulk is totally ignored by Penrose.