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*by John G. Cramer*

Sir Roger Penrose is an Oxford University superstar-theorist whose ideas have spanned an amazing breadth of territory, ranging from geometrical tiling to the nature of human consciousness to the structure of space-time. At age 87 he is still going strong, and for the last decade has been promoting and investigating a radical new theory, Conformal Cyclic Cosmology (or CCC), which is based on general relativity and which concerns itself with the origins of our universe and its predecessors. I find CCC to be a very interesting take on cosmology, but I’m afraid that it has some fatal flaws.

Basically, Penrose observes that during the evolution of an open Friedmann-Lemaître-Robertson-Walker universe like ours, starting from the initial singularity of the Big Bang and ending with infinite expansion to timelike infinity, there are two distinct eras in which the universe lacks any way of “building a clock” to measure time, and so time itself becomes meaningless. One of these eras is the initial singularity of the early universe, in which time is infinitely dilated by gravity. The other is the exponential expansion toward timelike infinity of the very late universe, the era after all protons have decayed to leptons, all black holes have evaporated into Hawking radiation, and all that remain in the expanding universal blackness are massless photons and gravitational radiation traveling at the speed of light. Massless wave-particles like electromagnetic and gravitational waves do not have “clocks” because they travel at light speed, so that in their rest fames time is completely halted. As we say in physics, if you travel at the speed of light, everything happens at once.

Because of this similarity in the “clocklessness” of these two eras, general relativity theorist Paul Tod pointed out in 2003 that the initial singularity of the Big Bang can be conformably mapped into the very late stages of infinite expansion populated only by massless particles. In some sense the two eras, even though vastly different in scale, represent the same timeless conditions. Penrose has extended Tod’s idea by taking the conceptual leap of asserting that this conformal mapping is not just an interesting similarity. Rather, it is a real and actual transition. This allows him to hypothesize the existence of an infinite “daisy chain” of universes, the very late stage of each predecessor universe transitioning into the initial Big Bang stage of the next universe in the chain.

It’s well known in cosmology that there is a severe entropy problem with all recycling universe models. This is because the Second Law of Thermodynamics requires that the entropy of the overall system must always progressively increase with time. That implies that every successive universe in such a cyclic chain must have more entropy and be more disordered than its predecessors.

In the early Big Bang stage of our universe, the gravitational degrees of freedom were very small and restricted, leading to great uniformity in all regions and very small initial entropy. Penrose argues that the enormous rescaling compression that occurs in the conformal remapping across the boundary from late infinite expansion to initial Big Bang singularity resets the entropy of the emerging universe to a very small value and also accounts for the remarkable uniformity of the early universe. Interestingly, this scenario eliminates the need for assuming an inflationary phase in the early universe, as is hypothesized by the current ΛCDM Standard Model of cosmology to account for that uniformity. In other words, the conformal transition of CCC resets the entropy to a very low value.

Penrose assumes that the massless speed-of-light “clockless” particles of each previous universe cycle are carried over to the next cycle, while any massive particles (those with internal clocks) are removed by decay, particle-antiparticle annihilation, or capture by black holes, so that they do not participate in the transition to the next cycle. The transferred massless particles (photons, gravitons) are integer-spin bosons, while the non-transferred particles with mass (electrons, neutrinos) are fractional-spin fermions. I see some serious problems with Penrose’s assumption of the vanishing fermions, which will be discussed below.

* * *

The big problem with most attempts to construct any general theory of cosmology, particularly one as extrapolative as CCC, is that there are typically no experimental or observational tests that can be used to check on validity. Rather remarkably, this is not the case for CCC. One CCC test is that there should be no great outburst of gravitational radiation, as the standard-model inflation scenario in the early Big Bang would produce. The BICEP2 experiment in Antarctica is presently searching for the polarization signature of such gravitational radiation from inflation but, consistent with CCC, has not observed it. In a sense, CCC also includes inflation, but its inflation occurs late in the previous cycle of the universe, before the conformal remapping occurs and before the first stages of the Big Bang, and thus it leaves no gravitational wave signature.

Further, in the late stages of the hyper-expanded previous universe, the very massive black holes from the centers of dead galaxies would collide, making gravitational radiation, and ultimately would evaporate into Hawking-radiation photons, producing clumps of leftover photons and gravitational waves. The resulting clumps would be carried into the next cycle of the universe chain, producing a clumping that Penrose calls “Hawking points” that cause disturbances in the cosmic microwave radiation. These Hawking points are supposed to appear in the temperature variations of the cosmic microwave background as a pattern of concentric circles.

Penrose and his colleagues claim that their analysis of WMAP and Planck data has found such concentric circles in with significance of 6-sigma or more, as compared to simulations based on standard ΛCDM cosmology (cold dark matter with cosmological constant Λ). However, several other groups have attempted to reproduce this analysis and have found no statistically significant indication of the Hawking-point circles. The difference seems to revolve around the way in which the individual groups did the ΛCDM simulations. In a recent publication, Penrose and collaborators further claim that the polarization-dependent B-mode observations of the BICEP2 experiment provides an additional indication of Hawking points in the cosmic microwave background. The controversy about the presence or absence of Hawking points in the cosmic microwave background radiation continues, and we will have to wait for some time to see if the physics community accepts Penrose’s analysis as supporting his CCC description of the universe.

To make CCC work, Penrose needs to introduce some specific assumptions about the dark matter in the universe: what it is and how it dissipates in the late stages. He assumes that our universe’s dark matter is formed of previously unknown massive particles that he calls erebons, which are purely gravitational, have no strong, weak, or electromagnetic interactions, have a rest mass on the order of a Planck mass (21.8 μ*g* = 1.221028 eV), a lifetime of around 1,011 years, and ultimately decay into Planck-energy gravitational waves. Penrose depends on these hypothetical dark matter leftovers to provide just the right amount of temperature variation, as observed in the cosmic microwave background.

* * *

There are problems with the CCC scenario. In order for the late phase in which the universe undergoes infinite expansion to timelike infinity to match the “clocklessness” of the initial Big Bang singularity so that one can be conformably mapped into the other, the late-stage universe must be completely empty of all massive particles. In particular, one must assume that all protons eventually decay into leptons. Further, Penrose’s late-stage universe must somehow have also eliminated all of the electrons, positrons, neutrinos, anti-neutrinos, and dark matter particles that were previously present in great numbers.

Neutrinos are among the most plentiful particles in the universe because there was a weak-interaction flash of neutrinos created in the early Big Bang in analogy with the flash that created the cosmic microwave background. These very low energy cosmic background neutrinos are everywhere around us in great numbers, and there is no established mechanism for getting rid of them as the universe ages. Penrose proposes to deal with them by hypothesizing a fourth species of neutrinos that is massless. He requires that the three species of massive neutrinos should decay into the massless neutrino variety as the late-stage universe ages to timelike infinity.

The large population of electrons and positrons in our present universe represents a more serious problem for Penrose’s CCC. Along the path to timelike infinity, many of these electrons and positrons will pair off and annihilate into photons, but as Penrose points out, many will be trapped at or near the event horizons of black holes. Further, the Hawking evaporation of black holes with a net electrical charge will produce even more electrons or positrons. One cannot get away with hypothesizing that over the long haul all the electrons and positrons decay into some hypothetical massless particles because such particles would have an electric charge. There are no known stable massless charged particles. They cannot exist because an electric charge moving through space at the speed of light would radiate away all its energy into Cherenkov radiation.

Penrose has this to say about the electron problem: “There are various possible ways out of this, none of which is part of conventional particle physics. One possibility is that electric charge is not exactly conserved, so that within the span of eternity electric charge would eventually disappear. A much more satisfying possibility, from my own perspective, is that the electron’s mass would eventually decay away—and again there is all eternity for this to happen, so the possibility may not be too outrageous to contemplate.”

I find Penrose’s attempts to wriggle out of the electron problem curious and unacceptable. Most physicists would certainly choose to retain electric charge conservation and to dump Penrose’s CCC model, rather than the other way around. Further, the suggested fix to CCC of decaying away the electron’s mass does not solve the charge problem; it only converts electrons to massless light-speed charged particles, which as noted above cannot exist.

In summary, Sir Roger Penrose’s Conformal Cyclic Cosmology is certainly provocative, offers much food for thought, and solves some of the problems of standard cosmology, e.g., inflation and dark matter, in interesting ways. It may or may not be supported by the observation of concentric circular patterns in the temperature variations of the cosmic microwave background. However, it has problems of its own, e.g., the electron problem, and these make it very difficult for me to take CCC seriously as a model of the universe.

**References:**

*Conformal Cyclic Cosmology:*

Roger Penrose, “Before the big bang: An outrageous new perspective and its implications for particle physics,” Proceedings of EPAC 2006, Edinburgh, Scotland, 2759—2767 (June 2006); available at *https://accelconf.web.cern.ch/accelconf/e06/PAPERS/THESPA01.PDF*

*Concentric Circles in CMB:*

V. G. Gurzadyan and R. Penrose “Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity”, (2010-11-16); arXiv:1011.37061486 [astro-ph.CO].

V. G. Gurzadyan and R. Penrose “More on the low variance circles in CMB sky”, (2010-12-07), arXiv:1012.1486 [astro-ph.CO].

I. K. Wehus and H. K. Eriksen, “A search for concentric circles in the 7-year WMAP temperature sky maps”. The Astrophysical Journal 733 (2), L29 (2010); arXiv:1012.1268 [astro-ph.CO].

A. Moss, D. Scott and J.P. Zibin, “No evidence for anomalously low variance circles on the sky”. Journal of Cosmology and Astroparticle Physics, 2011 (4), 033 (2010); arXiv:1012.1305 [astro-ph.CO].

A. Hajian “Are There Echoes From The Pre-Big Bang Universe? A Search for Low Variance Circles in the CMB Sky.” The Astrophysical Journal. 740 (2), 52 (2010). arXiv:1012.1656 [astro-ph.CO].

A. DeAbreu, et al, “Searching for concentric low variance circles in the cosmic microwave background”, Journal of Cosmology and Astroparticle Physics 2015 (12), 031 (2015); arXiv:1508.05158 [astro-ph.CO].

Copyright © 2019 John G. Cramer

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