Penrose's Cyclic Cosmology

By Sean Carroll | December 7, 2010 10:09 am

Update: Gurzadyan and Penrose have very quickly put up a response to the analysis papers quoted below. And another paper critical of G&P has appeared, by Amir Hajian.

Gurzadyan & Penrose Roger Penrose and his collaborator Vahe Gurzadyan made a splash recently by claiming that there was evidence in the cosmic microwave background for a pre-Big-Bang era in the history of the universe. (Here’s the paper.) The evidence takes the form of correlated circles in the cosmic microwave background anisotropies, as pictured here. They claim that they have found such circles at a level of significance much higher than would be predicted in a conventional scenario, where perturbations were random and uncorrelated on various scales.

That would be pretty amazing, if true. But it looks like it isn’t. Here are two skeptical papers that just appeared on the arxiv. (Hat tip to David Spergel. Peter Coles was an early skeptic.)

A search for concentric circles in the 7-year WMAP temperature sky maps

Authors: I. K. Wehus, H. K. Eriksen

Abstract: In a recent analysis of the 7-year WMAP temperature sky maps, Gurzadyan and Penrose claim to find evidence for violent pre-Big Bang activity in the form of concentric low-variance circles at high statistical significance. In this paper, we perform an independent search for such concentric low-variance circles, employing both chi^2 statistics and matched filters, and compare the results obtained from the 7-year WMAP temperature sky maps with those obtained from LCDM simulations. Our main findings are the following: We do reproduce the claimed ring structures observed in the WMAP data as presented by Gurzadyan and Penrose, thereby verifying their computational procedures. However, the results from our simulations do not agree with those presented by Gurzadyan and Penrose. On the contrary we obtain a substantially larger variance in our simulations, to the extent that the observed WMAP sky maps are fully consistent with the LCDM model as measured by these statistics.

No evidence for anomalously low variance circles on the sky

Authors: Adam Moss, Douglas Scott, James P. Zibin

Abstract: In a recent paper, Gurzadyan & Penrose claim to have found directions on the sky centred on which are circles of anomalously low variance in the cosmic microwave background (CMB). These features are presented as evidence for a particular picture of the very early Universe. We attempted to repeat the analysis of these authors, and we can indeed confirm that such variations do exist in the temperature variance for annuli around points in the data. However, we find that this variation is entirely expected in a sky which contains the usual CMB anisotropies. In other words, properly simulated Gaussian CMB data contain just the sorts of variations claimed. Gurzadyan & Penrose have not found evidence for pre-Big Bang phenomena, but have simply re-discovered that the CMB contains structure.

The basic message is simple: sure, you can find some circles in the sky if you look there. But they are simply what you would expect from random alignments, not a new signal over and above the usual predictions. The authors here are respected CMB analyzers, and I strongly suspect that they are correct. Which reminds us of an important lesson: analyzing the CMB is hard! It’s a very messy universe out there, and if you don’t take every single source of error correctly into account, you can convince yourself of all sorts of things.

Just because this particular signal is there doesn’t mean the underlying model — Penrose’s Conformal Cyclic Cosmology (CCC) — isn’t right. I’m all in favor of pre-Big-Bang cosmologies myself, and Penrose more than anyone has been correct in insisting that the low entropy of our early universe is a crucial problem that is not well-addressed in modern cosmology. But I’ve been hesitant because, frankly, I don’t really get it.

As far as I know, there isn’t any exposition of the CCC in the form of a freely-available technical paper. There is a book, which hasn’t officially been released in the U.S. but you can get your hands on if you try hard enough, which I did.

Roger Penrose, Cycles of Time: An Extraordinary New View of the Universe

Even with the book in my hands, however, I can’t quite discern the underlying physical mechanism that makes it all work.

The basic point is this. The very early universe is smooth. The universe right now is lumpy, with stars and galaxies and black holes all over the place. But the future universe will be smooth again — black holes will evaporate and the cosmological constant will disperse all the matter, leaving us nothing but empty space. (Just wait about 10100 years.) So, Penrose says, we can map the late universe onto a future phase that looks just like our early universe, simply by a conformal transformation (a change of scale). Do this an infinite number of times, and you have a cyclic cosmology — the universe goes through a series of “aeons” that start with a smooth Big Bang, get lumpy as structure forms, smooth out again, and then gets matched onto another smooth Big-Bang-like phase, etc.

If you’re sketchy on that last bit, join the club. Sure, mathematically we can map the smooth late universe onto the smooth early universe. But what physical process would actually cause that to happen? Despite having the book in my hands, I’m still unclear on this. (I absolutely confess that the answer might be in there, but I simply haven’t read it carefully enough.) While the early and late universes are both smooth, they are very different in other obvious ways, such as the energy density. What causes the low-density late universe to come alive into something like the high-density early universe? Something like that happens in the Steinhardt-Turok cyclic universe, but in order to make it happen you need to specify some particular matter fields with very specific dynamics. This isn’t a trivial task; there are things you can try, but they generally are plagued by instabilities and singularities. I don’t see where Penrose has done that, so I’m not even sure what there is to be criticized.

Regardless, I am highly skeptical of cyclic cosmologies no matter what flavor they come in. The most obvious empirical fact about our observable universe is its temporal asymmetry — the early phase is very different from the late phase, even though no such difference is to be found in the fundamental laws of physics. (I wrote a book about this, if you’re interested — Roger Penrose blurbed it.) Our goal should be to explain that asymmetry. But cyclic cosmologies simply extend it over an infinite number of cycles, without any explanation. If you took a typical state of the universe today and played it backwards in time, you wouldn’t expect to get anything like these cyclic cosmologies; it would just collapse into a mess. What you would need to do is argue that this kind of behavior arises robustly from a wide variety of possible initial conditions. If you need some special conditions, fine — but you’re not doing any better than the ordinary Big Bang.

CATEGORIZED UNDER: arxiv, Science, Top Posts
  • Aaron Sheldon

    Just goes to show that even the best of us can get bitten by underestimating the potency of Probability Theory and the effect of randomness.

    I would have thought that a cyclic universe scenario actually confounds the paradox of temporal asymmetry? At least with a single big bang scenario there is a boundary in time to move away from.

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  • Josh

    “The universe goes through a series of “aeons” that start with a smooth Big Bang, get lumpy as structure forms, smooth out again, and then gets matched onto another smooth Big-Bang-like phase, etc.”

    I believe Penrose is making a unification argument here. He’s saying that the two epochs are identical and related through something like gauge transformations. Penrose doesn’t seem take the concepts of singularity nor infinity seriously. He considers those to be precisely the same things. In that way, he totally sidestepped the issues that plague the cyclic model.

    Can infinity equal zero? I’m not sure. If I could think of some physical analogy that worked like this, I might be more convinced. But I think I agree with Sean that this mathematical trickery as beautiful and simple as it is seems to lack a certain physicality. Of course, if actual co-centric circles had been found then I might have taken him seriously.

  • psmith

    Thanks for clarifying this. I am reminded of one of your sayings – ‘extraordinary claims require extraordinary evidence’. For me this failed when I considered the implications of multiple concentric circles.

  • psmith

    Sean, you say ” I’m all in favor of pre-Big-Bang cosmologies myself”, why? Is this a philosophical stance?

  • Sean

    It’s because I think pre-Big-Bang cosmologies have the best chance of explaining the low-entropy conditions of the observable early universe.

  • spyder

    I find it interesting that Penrose chose to ascribe the meaning of aeon in its Sanskrit formulation rather than the ancient Greek. Not wanting to make any claim per se, but it does seem to me that the ancient Hindu cosmology has more in common with the Penrose (CCC) universe than with the CMB.

  • Torbjörn Larsson, OM

    [smug] I said as much already:

    So 6sigma is what is reported, or referenced here. This is enough to raise eyebrows.

    It shouldn’t, and it doesn’t raise my eyebrows.

    It is 6 sigma against the modeled background vs the pattern, but not any uncertainty of *finding* the pattern in the first place. You will fit square patterns, flower patterns, three [sic] patterns and your grandma’s face against a gaussian background.”

    Penrose may have seen his grandma. [/smug]

    Wehus et al produces exactly the test statistic (as a comparison) I asked for. And Moss et al checks for, if not faces, so triangular patterns. Yay!

  • Josh Neal

    Sean, can you give an example of a pre-Big-Bang cosmology that would explain the low-entropy conditions of the observable early universe? It can be entirely speculative; I won’t hold you to it.

  • Sean

    There’s one in my book, or in my paper with Jennie Chen. We try to explain the low entropy, although success is of course in the eye of the beholder.

  • Timon of Athens
  • ad

    Let me get this straight: Penrose et al say there are families of *concentric* circles discernable in the CMB, whern chance says there should only be *random* circles. Two groups do their own analysis and say: yes, there are circles in the the CMB like Penrose et al say, but this is exactly according to chance (like Penrose et al say) so therefore everything else they say is somehow wrong? I don’t get it, they neither confirm nor refute the existence of the *concentric* circles.

  • Bee

    Question: In Loop Quantum Cosmology the pre-bounce era leaves an imprint in the tensor-mode spectrum in form of a peak, see or, for a recent data analysis, I’m wondering now in how far this is a general feature of a bounce and in this respect model-independent rather than a feature of LQC? Ie, would one expect it to also be present in a Penrose-like scenario?

  • Eugene

    ha! I knew it! A posterior statistics strikes again.

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  • loveencounterflow

    i find it quite logical that the late universe should look like a mirror image of the early universe and have been conjecturing so for over ten years when i first discovered what was wrong about the common picture of the big bang which is commonly conceived of as a kind of very violent, very fast explosion.

    since, when matter and energy is confined to a very small volume, shouldn’t time run at a very slow rate? conversely, with matter and energy spread out infinitely thinned over an all-expansive volume, shouldn’t time run at a very fast rate? therefore, in the late universe, ‘time’ in the sense of ‘things happening’ more and more ceases to exist, as there is very little around to happen; yet time is also accelerated, which is like time speeds up so as to make the drive less boring, whereas in the early universe, time is very, very slow to give the huge number of densely packed interactions more temporal volume. it is like the temporal and spatial volumes (and maybe there are more) just oscillate in sync, like a sine and a cosine wave. imagine a film with action-packed scenes you want to watch in slow motion (slower time, more temporal space in terms of wall time) and long uneventful stretches you want to view in time lapse (fast time, less temporal space); the net effect is that, in terms of wall or viewing time, the entire movie shows about the same number of events per tick of the clock.

    also, in an all-diluted cosmos, you cannot say where you are or when you are in case a daemon should throw you there, as everywhere and everywhen looks very much the same—this is, essentially, the definition of a mathematical point, and very similar to an elementary particle: if i take away your electron and replace it with another one, you can never sue me as you can’t prove it: there are no pink electrons, and one electron looks exactly identical to the next.
    it is quite conceivable that the passing of time occurs in two directions, one stretching out from what we think of as the big bang towards a future of perfect dilution, and an opposite one where time runs from our point of dilution towards our big bang. the views that our future is the big bore (dilution) or the big crunch (implosion) are completely symmetrical and possibly quite undecidable.

  • TomC

    Two points about the rebutting papers and GP10′s response:

    1) Both rebutting papers basically confirm the presence of the signal found by GP10. However, they find that GP10 overestimate the significance of the effect by a factor of ~3. It turns out this is because when GP10 looked for the variance of similar measurements on simulated skies, they left the CMB unchanged and just randomized the noise. The rebutting authors (both groups) compared to simulations in which the CMB was also re-simulated. The fluctuations in the WMAP W-band maps are dominated by CMB, not noise, so this makes a big difference. In GP10′s response, they argue that their method is correct because: “[a] more appropriate procedure [is] to simulate an isotropic Gaussian signal, to see whether such circles are result of random fluctuations” (their emphasis). This is a strange use of “isotropic.” The Gaussian field generated in a CMB simulation is in fact isotropic (in the sense that only depends on the angular separation between n1 and n2, not the direction of the vector between them). Anyway, I think most CMB folks would agree that if you think an anomalous signal in the WMAP data is cosmologically important, you need to show that it would not be detectable in most random realizations of the best-fit CMB power spectrum. (I.e., I agree with the rebutting authors.)

    2) Both rebutting papers are looking specifically for concentric circles, and they find directions in their simulated skies that have families of concentric, low-variance circles which look qualitatively just like GP10′s signal. So I have no idea what that part of GP10′s response is referring to.

  • Sean

    TomC– completely agree. I couldn’t understand that use of “isotropic,” especially with the emphasis. Was someone simulating an anisotropic signal?

  • Ellipsis

    We now know where Roger Penrose has found his posterior.

  • Ben Schulz

    If one day we are able to create black holes I would hope that we could leave a message for a possible future universe. Perhaps something along the line of : The Universe is not random, nor infinite”

  • ObsessiveMathsFreak

    The CMB is becoming the astrological tarot of theoretical physics. It’s just one datum!

  • Cusp

    >The CMB is becoming the astrological tarot of theoretical physics. It’s just one datum!

    No it isn’t.

  • Julian

    @TomC & Sean

    Re the use of Isotropic (which I also thought obscure) – I think the answer is in this sentence in GP’s response to the rebuttals:

    “Both groups simulate maps using the CMB power spectrum for LCDM, while we simulate a pure Gaussian sky plus the WMAP’s noise”

    I understood this to mean (in the context of the interpretation) that if (but not IFF) LCDM is the null hypothesis, then it is falsified at only the 3 sigma level, but that if the null hypothesis is purely a Gaussian CMB plus instrument noise, then it is falsified at the 6 sigma level.

    In other words, the isotropy is in the power spectrum rather than spatial.

    However, since I have reason to doubt that I know what I’m talking about, feel free to skip ahead to a more enlightenting comment ;)

  • Aiya-Oba

    I see Penrose’s Conformal Cyclic Cosmology, very much intune with the eternal- ever- elusive underlying model, of self-Creation, evolution and equator of Spacetime-Continuum.

  • Aaron Sheldon

    The GP hypothesis would have probably been handily rejected if they had properly applied the Maximum Likelihood Ratio Test. Essential, they have introduced a hypothesis with an additional 10885 parameters (one for every tested circle center). A Chi-Square with 10885 degrees of freedom would have critical values so extreme that it would safely put all but the most dead obvious findings out of reach.

    Succinctly, their fundamental statistical error was failing to recognize that they were testing 10885 possible hypotheses, not one single hypothesis.

    Technically a straight forward application of the Expectation-Maximization Algorithm would be sufficient to find the Maximum Likelihood Estimators.

    Also, am I the only one who has noticed that the GP circles in the posted photo align nicely with the artifact birefringence patterns? That makes me really suspicious of the GP findings.

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  • Sili

    Has Penrose entered old age loonihood? Combined with his microtubular quantum consciousness nonsense, it’s hard not to see him as a latter day Pauling.

  • Bruys

    “Our goal should be to explain that asymmetry. But cyclic cosmologies simply extend it over an infinite number of cycles, without any explanation.”
    Here you are not being fair. Penrose makes it clear in his book that he is motivated to posit his theory precisely to explain that apparent asymmetry. Admittedly, in the process he goes way out on a limb, as you point out, because there is no explanation of how the conformal transformation occurs as a physical process. The conformal transformation seems to be more than a simple change of scale, too, as there is a sign change involved (you’d understand the mathematics better than I, he gives a summary in an appendix, whose complexity and condensed nature sit uncomfortably with the rest of the book). He would surely counter that the field(s) necessary to give rise to inflation in the usual inflationary picture are an arbitrary construction, that his theory avoids. He argues that inflationary theories do not provide an explanation for the low entropy state of the early universe, while his does. His explanation relies on the controversial prediction that the amount of entropy released by an evaporating black-hole is less than that consumed by its creation. There’s plenty to argue about, but you have to admire that he is trying put it to experimental test.

  • Phil Warnell

    While so many are quick to scoff at Penrose for his efforts, I would rather praise him for at least raising the general awareness regarding the problem and emphasising what things need to be addressed. I can’t help but think back to Copernicus where he was so concerned with challenging the prevailing paradigm he left the publishing of his findings until after his death. It’s also true that if later Kepler were to simply to look to his data which would serve to indicate Copernicus’s model must be flawed as it not being consistent with circular orbits, the general theme expressed in the model might have not been pursued any further as to have the old one to hold. This whole discussion has me mindful of what Milton said in “Paradise Lost” when it came to many of the sentiments expressed here.

    ”From man or angel the great Architect
    Did wisely to conceal, and not divulge
    His secrets to be scanned by them who ought
    Rather admire; or if they list to try
    Conjecture, he his fabric of the heav’ns
    Hath left to their disputes, perhaps to move
    His laughter at their quaint opinions wide
    Hereafter, when they come to model heav’n
    And calculate the stars, how they will wield
    The mighty frame, how build, unbuild, contrive
    To save appearances, how gird the sphere
    With centric and eccentric scribbled o’er,
    Cycle and epicycle, orb in orb.”

    -Milton, “Paradise Lost”

  • David Wilson

    No cosmologist myself but followed discussion of pre- big bang theories on TV programme and was intrigued by Penrose contribution – sufficiently intrigued to order The Cycles of Time from the library. Did reasonably well for the first 100 pages before losing the thread – not that this is in any more than an indication of my own limitations regarding hyperbolic geometries, tensors etc.

    I admire your openess in questioning the CMB analysis while leaving the door ajar on the theory itself. And I am reassured that you didn’t find the arguments in the book entirely conclusive – though, in your case, I am sure the incomprehension was of quite a different sort than mine.

    And i couldn’t quite believe my eyes recently when I saw Cycles of Time classed as Popular Science in a large London bookstore.

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  • Fivedoughnut

    Perhaps dark energy/cosmic expansion is simply an affect of a big crunch?

    Allow me to elucidate;- When a ‘crunch’ condenses below its Schwarzchild Radius, I propose a duality is formed, being the Lorentz Transform imaginary values associated with <Sr distances – we know time=0 at an event horizon; therefore, beneath this boundary, t becomes a dualistic positive/negative ….. basically, the inner convergence co-manifests as a recursive, out-riding expansion. This suggests our universe is cyclic /wavicle like and totally explains why the expansion rate is steadily increasing, as the condensing crunch produces exponetially increasing t/ti values.

    Even wilder speculation;- I believe every particle, even the humble photon may obey this simple process (implying – the universe is just another particle ) Shocked

    Energy convergence with regards to a photon, ultimately produces a singularity via its very own Schwarzchild radius (albeit at extremely small scale distance).

    i.e; If a photons relativistic mass (hf/c^2 – yes I know photons do not possess mass!) is substituted for M in calculating a Schwarzchild Radius: 2GM/C^2. This photon, say in the visible spectrum (around 600 THz) would produce a figure of about 10^-62 meters ……. totally smaller than planck length!

    The photonic cycle is one of 720° (360° positive/ 360° negative), in which convergence and expansion co-exist simultaneously.

    Expansion above the Sr can be thought of as the magnetic component. Similarly, condensation beneath; manifests as the electric component. Thus, this duality operates with 180° phase differential, perfectly matching/describing electromagnetism, with each swapping identities @ the Sr 'boundary'.

    An electron/ positron pair;- perhaps a ring singularity to hypertorus cycle, embedded in the expanding wavefront surface of our universe, with photons themselves, as integrated wavicles within a facet of their overall electro-positronic wave-state …. 'riding around' hyperspace.

    Musing on ….. your average photon cycles a tad more rapidly than our universe, say 300Ghz compared to maybe once in a trillion years – how can this be so? ….. well, it's all to do with dimensionality. With increasing dimensionality, energy is sprawled about ridiculously thinner;- so what of our universe, an expanding wavefront of possibly hypertoroidal topology?;- our universe of high order dimensionality may have energy spread out rather sparse ….. it's energy concentration that determines frequency, just like low energy photons cycle slower than high ones. Photons, despite having astoundingly less energy than the universe, have absolute lashings to play about within their far lower dimensional wave-space realm.


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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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