This is the third installment in my discussion of bouncing and cyclic cosmologies, and the first of a two-part treatment of Roger Penrose’s Conformal Cyclic Cosmology. It is timely because it fits into a discussion that has been unfolding over the past year in various books and podcasts. For me at least, it’s also a bit nostalgic, since the profound disagreement I have with Penrose’s recent cosmological theory is framed by friendly interactions with the man himself a quarter century ago. Let me elaborate.
Some History
The backdrop for my current foray is provided by two books that pull readers in opposite directions. The first is Stephen Meyer’s Return of the God Hypothesis, which presents the evidence for a cosmic beginning and explains how multiple attempts to explain it away all carry a substantial cost. The second book, Niayesh Afshordi and Phil Halper’s Battle of the Big Bang, is a survey of 25 different cosmological models that attempt to obviate the need for a beginning and suggest another way forward. Interestingly, the situation is reminiscent of another, forty years ago, when two books pulling in opposite directions, Richard Dawkins’s The Blind Watchmaker and Michael Denton’s Evolution: A Theory in Crisis, catalyzed Phillip Johnson to write Darwin on Trial, and much of consequence ensued in discussions of biological origins. It’s not that these discussions were not already taking place; it’s that they grew in both quantity and quality of interaction. Similarly, the current foment in cosmological discussions suggests that an ongoing dispute is gaining new vigor and that much of consequence may ensue. The waters of cosmological fine-tuning are reaching a slow boil, and with the question of cosmological origins drawing heat again, we may be poised for a phase change in the quantity and quality of interactions on these subjects. The dueling cosmological prognostications of Meyer versus Afshordi and Halper, and the recent theater run of the documentary The Story of Everything, are certainly adding fuel to the fire.
The match lighting this latest fire was struck when Meyer, on a podcast with Sean McDowell, made a passing comment criticizing Penrose’s model. Halper flagged the criticism for Penrose and he replied in defense of his model. This separate give-and-take provided the impetus for a three-hour debate moderated by Justin Brierley late last year (which did not air until a few weeks ago), after which Halper assembled a panel of physicists to respond to Meyer. Steve has since appeared on McDowell’s podcast twice, first to clarify what his argument actually is in light of Halper’s mischaracterization, and then, in the interview to which this essay is most closely related, to walk through Penrose’s model systematically, showing, with quotations from Penrose himself, where it succeeds as mathematics and fails as physics. I will be doing the same thing here, but more comprehensively and, in the second essay, by extending the critique to new territory.
Now, a word about the “ancient” history of my personal contact with Penrose and the spirit in which this criticism is offered. My engagement with his views began in graduate school with courses on the foundations of cosmology, quantum mechanics, philosophy of mind, and mathematical logic during my doctoral studies at Northwestern University, culminating in a dissertation on the historical and philosophical foundations of quantum statistical mechanics. After a post-doctoral stint at the University of Notre Dame, my first academic appointment was at Baylor University as the resident philosopher of physics and associate director of the short-lived Michael Polanyi Center for Complexity, Information, and Design, after which I served as director of the program in science, philosophy, and religion for a few years. In 2002, I conceived and, with the help of the Baylor Physics Department and funding from the NSF and a consortium of Texas physics departments, coordinated the Dirac Centenary Conference marking the hundredth anniversary of Dirac’s birth. When the conference convened on the Baylor campus for three days in the fall of 2002, I had the honor of hosting Penrose as a featured speaker, alongside other luminaries in physics and mathematics like John Polkinghorne, Gordon Kane, David Olive, Richard Dalitz, Laurie Brown (see also here), John Roberts, Cumrun Vafa, and John Roe, and philosophers of physics Simon Saunders and Michael Dickson. A few years later, Penrose and his collaborator, Stuart Hameroff, contributed an updated essay on their thesis that consciousness arises from quantum processes in the brain to a volume that I edited with William Dembski, The Nature of Nature: Examining the Role of Naturalism in Science (ISI Books, 2011). This massive collection grew out of a conference of the same name that the two of us had organized at Baylor University a decade earlier. I mention all these things to make it plain that the criticisms I offer come out of a long familiarity with Penrose’s work and a genuine admiration for his many accomplishments.
Returning, then, to the role of this essay as the third installment in a series, by way of quick review, I remind the reader that the first installment focused on bouncing and cyclic cosmologies in general and various attempts to avoid the conclusion that such models cannot be past-eternal. These evasion strategies included models as diverse as those involving bouncing branes, entropy-avoiding bounces, an asymptotically flat past (potentially followed by successive bounces), and selective changes of conformal frame. These escape efforts were found either to fail or be plagued by intractable or insurmountable difficulties arising from the kinematic Borde-Guth-Vilenkin (BGV) theorem, Aron Wall’s thermodynamic quantum singularity theorem, the Tolman entropy problem, the Kinney-Stein result, the Mithani-Vilenkin instability proof, and more general problems related to quantum instability. The second installment of the series turned to loop quantum cosmology, the most interesting research program in quantum gravity and cosmology, which replaces the big bang with a “big bounce” that results from its treating space as discrete at the smallest scale. Alas, it too cannot cycle forever, since entropic book-keeping closes down every potential avenue of escape.
This brings us, at last, to the remaining “cyclic” proposal, that of Roger Penrose, which is perhaps the most quixotic of all. Conformal cyclic cosmology (CCC) purports to offer an endless cycle of cosmic “aeons” with no bounce at all. As we will see shortly, it cannot readily do so because the device meant to achieve this goal is a conformal maneuver reminiscent of that which undid the Bars-Steinhardt-Turok (BST) cyclic cosmology we considered in the first installment. Despite this, Penrose deserves credit for his creative use of conformal geometry, because his model preceded BST, even though it leads nowhere for the same basic reasons.
With these things in mind, there is an irony in the title of both this third essay and the fourth and final one in this series. As I take up an examination of CCC under the heading of fashion and faith, followed by a consideration of it as mathematical fantasy, I allude to Penrose’s own reflections on the state of cosmology. In 2016, he wrote a book titled Fashion, Faith, and Fantasy in the New Physics of the Universe in which he diagnoses the ailments of modern theoretical physics in three broad categories — a fashionable preoccupation with string theory, a strong faith that quantum physics may be applied unchanged to the universe at the largest scales, and fantastical cosmological speculations untethered from substantial evidential constraint. I think his diagnosis has much merit. He is even so candid and self-deprecating in this book as to describe his own CCC model as “conformal crazy cosmology.” His humility and willingness to poke fun at himself are among the many reasons he is so well-liked and admired. I intend no disrespect when I quote him in this regard; I only mean to take his joke more seriously than he did, showing how all three of the pathologies he identifies recur under different guises in his own ambitious proposal.
A Maneuver We Have Seen Before
Since Penrose’s argument hinges on conformal transformations, let’s have a brief reminder of what such transformations accomplish. Conformally rescaling the mathematical description of spacetime multiplies the way that distances are measured at each point by a smooth, positive factor. Doing this retains all angle measurements and the causal order of events while rendering the model insensitive to all measurements of distance and duration, including those of infinite extent.1 It is a change of units deliberately designed to ignore scale.
In the first installment, we saw how Bars, Steinhardt, and Turok used this metrical indifference to reframe general relativity so that the Higgs field bestowed particle masses and the units of length and time could be stretched or shrunk from one place to another without changing any physical predictions. Cycle-ending crunches were thus conformally rescaled into a frame where masses would rise toward the Planck scale as the universe grew small, so a worldline could be drawn through the place it would formerly have ended. There being no past-incomplete geodesics in this representation, the BGV theorem was proclaimed irrelevant, and the universe to have no beginning to its existence.
As was noted when discussing the BST model, the conformal freedom doing the heavy lifting was manufactured rather than discovered. Its instantiation in the model came from the addition of a field that had the sole purpose of providing the needed adjustments to the absolute scales that ordinary physics holds fixed. The authors freely admitted that if this (ad hoc) field were held constant, their theory would collapse back to ordinary general relativity with a real curvature singularity at the crunch and the BGV theorem fully applicable. Adopting a description in which a beginning is invisible and then announcing that no beginning exists conflates an artifact of the description with a feature of the world. The question of a universal beginning can only be settled by examining the scale of proper time along worldlines and whether the curvature of spacetime becomes infinite. These are exactly the quantities a conformal frame is designed to ignore. When we dealt with the BST maneuver we remarked that we would encounter its cousin when we met with Penrose’s model. That time has now arrived.
What Penrose Asks Us to Believe
Conformal cyclic cosmology grew out of an observation made in the late 1980s by Paul Tod, a former doctoral student of Penrose’s at Oxford. Particle energies dwarf their rest masses to such an extent in the extreme furnace of the early universe that those masses become negligible and the universe can be described as if scale were irrelevant. What Tod noticed was that, in a scale-free (conformally invariant) description, the apparent absolute beginning of the big bang singularity smooths out into an ordinary past boundary. Penrose took this observation, and when it was discovered in 1998 that cosmic expansion is accelerating, put these two puzzle pieces together to frame his hypothesis. Since the universe can never recollapse if it is driven apart by dark energy, in a future that is unimaginably remote, if all matter decays or falls into black holes that themselves evaporate, nothing will be left except massless radiation, which is again a regime that is conformally invariant. Penrose thus decided an audacious proposal was in order: what if the massless remote future of one cosmic aeon were simply the big bang of the next, so that aeons could be joined together without any bounces by a conformal rescaling at a “crossover.”
There are some things that Penrose definitely gets right in all of this, which is why his proposal deserves serious engagement. The fact is that the very early universe was astoundingly gravitationally smooth and uniform when it could instead have been clumped and chaotic. Penrose himself quantified this extraordinarily low-entropy state, estimating its odds of arising by chance as one in ten to the power of ten raised to the 123rd power. This is the most extreme fine-tuning in all of known physics, and as he rightly observes, it begs explanation rather than just assumption as an initial condition. He is furthermore right that inflationary cosmology presupposes the very smoothness it is invoked to explain and compounds the fine-tuning problem in the process. And he is right that multiverse proposals merely redistribute this difficulty. What Penrose attempts to do with CCC is make this low-entropy state a structural necessity of the cyclic framework rather than a freakishly fine-tuned quantity. If CCC succeeded, it would be a major advance in our physical understanding of the universe, but it does not, and we may aptly, by way of irony, give the avuncular Penrose a friendly tweak by categorizing the reasons for its failure as fashion, faith, and fantasy.
Fashion
What is fashionable about conformal cyclic cosmology is its elegant mathematical aesthetic. Penrose is a consummate geometer, and CCC is first-rate geometry and only secondarily physics. Its cyclic ambitions also belong to a broad and self-referentially recurrent fashion, a Nietzschean penchant for dispensing with creation by eternal recurrence that has afflicted cosmologists for over a century; it is an infatuation that still makes cosmologists’ hearts beat faster, with no sign that the trend is waning. Penrose’s distinctive sartorial taste in cosmology finds its place in his conviction that a sufficiently elegant geometric structure might serve just as well as a physical mechanism. When the conformal description pulls away from the physical facts, the description is given primacy and reified with a causal power it does not possess. The mathematical construct is elegantly dressed up, but ultimately has no place to go.
There is a sharper irony that lies in wait here. Penrose smooths out the far future of each aeon with exponential dark-energy expansion so that all structure thins to nothing before the crossover. Viewed from the aeon that follows, this accelerated expansion is just an episode of inflation under another name right before the big bang. Penrose admits as much in his 2025 paper with Krzysztof Meissner. He states that the previous aeon’s exponential expansion “behaves, in effect, like an inflationary phase,” crediting to this prior expansion the near scale-invariance that standard inflationary cosmology credits to an early inflationary epoch. What is more, Jow and Scott’s (2020) published analysis of the Planck data finds “no statistically significant evidence for the presence of Hawking points” in the CMB, which is the one distinctive signature of CCC that is supposed to set it apart from inflation. A model built to dispense with the fashion of inflation has thus quietly changed its costume and is strutting down a different runway. This costume change is pricey. An inflationary phase, as Penrose himself has cogently argued, is entropy-increasing, and I will argue in the second part of this essay that putting such a phase before each crossover increases the bite of the radiation-entropy problem on which conformal cyclic cosmology ultimately founders.
Faith
Fashion may govern the style of CCC, but it is faith that determines its content. There are several commitments without which the model cannot function, and they are embraced, not because the evidence compels or even suggests them, but because the whole edifice collapses otherwise.
The first article of faith is that information is genuinely destroyed when a black hole evaporates. This runs contrary to the majority view among physicists, so let’s briefly examine what is at stake. The question turns on two things that the word “entropy,” used generically, runs together. The first is the familiar coarse-grained thermodynamic entropy characteristic of everyday disorder that the second law permits to climb. The second, lesser known among non-physicists, is the fine-grained von Neumann entropy of the quantum state itself, which remains constant, preserving information about the quantum state as long as the wavefunction evolves in the smooth and reversible way that physicists call unitary. The unitary evolution of the wavefunction is extraordinarily important to the integrity of quantum mechanics since it preserves total energy, angles and distances between quantum states and ensures that the total probability adds to one, while the unitary evolution generated by a closed system’s Hamiltonian further conserves energy and the symmetries from which the conservation laws flow. Unitarity conserves information so that a state that begins pure remains pure and a state that is mixed retains its precise mixture; nothing is ever erased in this regard, no matter how high the thermodynamic disorder rises. Destroying information breaks reversibility and turns pure states into ones that are genuinely mixed, which is exactly what CCC requires. All of the gravitational entropy collected over the entire history of the aeon has to be wiped clean before the next aeon can begin.
Penrose’s means of securing this outcome is to stipulate that whatever falls into a black hole disappears and ultimately is annihilated when that black hole evaporates. Nothing is preserved. It seemed that Hawking’s early calculation supported this viewpoint, because the radiation escaping a black hole looked purely thermal, as if the infalling information were simply erased from the universe. However, the theoretical physicist Don Page showed that if the evaporation is actually reversible, the radiation’s own entropy cannot rise forever. Rather, it climbs to a maximum and then falls back to zero as the hole evaporates, following what is now called the Page curve. This turnover has been recovered in recent work within gravity itself, so the prevailing view, contrary to Penrose, is that information survives and quantum mechanics is kept intact while our picture of spacetime dissolves. This stance thus pits Penrose against every major program in quantum gravity, since string theory, loop quantum gravity, and the holographic dualities of AdS/CFT all retain unitarity and reversibility. The lesson here is that Penrose does not derive the failure of information conservation from any deeper principle; he asserts it because CCC requires it to be true.
The second article of faith, if you’ll pardon the pun, requires taking mass — more precisely, it requires taking mass away. In order for the far future to be scale-free, no particle can retain its rest mass since every massive particle defines an intrinsic length scale, its Compton wavelength, which destroys the conformal invariance on which CCC depends. But how could the universe shed all its mass and reach a massless state? Massive particles cannot decay outright because the lightest electrically charged particle, the electron, stands in the way. It cannot decay without violating the conservation of electric charge, something for which there is absolutely no evidence or motivation. On the other hand, if all matter is conjectured somehow to be gathered into black holes that evaporate without a trace, then this would at best be an asymptotic state of the infinite future, with the universe approaching a massless state without ever arriving there. But an almost massless universe is still not conformally invariant, so the conditions for the CCC crossover are never met. Given that particle decay and black hole absorption are dead ends, Penrose is driven to the truly extraordinary thesis that rest mass effectively fades to nothing over cosmic time. This claim runs against the grain of all established physics. No mechanism exists for such a fade-out of mass. Its very conjecture is a blind leap of faith not just beyond what is evidenced, but contrary to what is evidenced.
A third faith commitment is to the low-entropy condition itself. Penrose calls this condition the Weyl Curvature Hypothesis (WCH). The hypothesis requires that the purely gravitational part of spacetime curvature must, for all practical purposes, be zero at the start of each aeon. It is important to recognize that while CCC tries to make this plausible, it is not derived in the model but rather asserted as a condition at every crossover. After the crossover, in order to furnish the new aeon with its needed dark matter and provide the seeds for cosmic structure, Penrose conjectures particles called erebons, hypothetical entities of approximate Planck mass that only interact gravitationally and which decay into gravitational waves (gravitons). The properties of these erebons are stipulated to meet the needs of the model, their abundance is fine-tuned to deliver the dark matter density we observe, and it hardly needs to be said that there is no independent physics pointing to their existence. In an effort to make contact with reality, Penrose proposed that erebon decay provided an explanation for certain anomalous-looking LIGO noise, but later analysis revealed that the effect was not statistically significant, so invoking the elaborate erebon hypothesis was rather like killing a non-existent gnat with a sledgehammer. Given this situation, even Penrose himself acknowledges that his whole scheme “needs a better theory” and “more calculations” to say why erebons should decay into gravitons and later re-form.2
The matter of fine-tuning the abundance of erebons is the point on which Penrose and Meyer have collided most directly. It is worth discussing, because Penrose’s response was quite blunt: “I have no idea what he’s talking about. There isn’t any fine-tuning of this sort.”3 Penrose is quite evidently sincere in this remark, and it’s clear that he never considered calculating fine-tuning in this respect. But this does not mean it isn’t built into the model. CCC requires the smoothness of the gravitational field at each crossover to match the boggling precision of the low-entropy big bang it is supposed to explain. This is the WCH assumed, not derived, and it is extraordinary fine-tuning. It requires the erebonic field to generate just the right quantity and combined mass of dark matter to regulate each aeon’s expansion so that galactic structures can form and the cosmos neither flies apart nor collapses in on itself. This also requires precise fine-tuning. These factors are not trivial incidentals; they are conditions that must be satisfied for the model to function at all.
Asked what he really believes about the low-entropy beginning with gravitational disorder so thoroughly suppressed, Penrose says his model is “trying to make it look natural” as the “continuation of the remote future of a previous [aeon].” He goes on to grant “you need some good reason from physics why this universe happened to have all these gravitational degrees of freedom not present in the early state. So you need a theory for that. You don’t need to say a creator did it.”4 In characterizing CCC as trying to make these conditions “look natural,” he is admitting that in themselves they are not natural, and a lot of weight is borne by the word “trying.” In saying “you need a theory for that,” he is also admitting that his model does not supply one. Calling the low-entropy state and erebonic dark matter regulation of cosmic expansion “natural” is a promissory note, not an explanation. The Weyl Curvature Hypothesis is reimposed at each crossover by fiat, and the erebonic field, which might have any value, is fine-tuned to regulate the expansion of the universe and the formation of its structures. Ultimately, Meyer’s distinction is the one that counts: Penrose did not calculate the fine-tuning, but he certainly modeled the need for it. To be charitable, theorists focused on making their mathematics come out right can miss what their constructions are implicitly demanding of reality. We see this in science all the time, and that is what seems to have happened here.
There is a poignant irony here that is hard to miss. Penrose accuses physicists who defend the conservation of information of having faith in the supremacy of quantum theory. Yet this faith is grounded in the extraordinary accuracy of quantum theory in the realms where it can be measured, along with calculations that demonstrate how it might be extended to address the question of black hole information. In the case of Penrose’s counterproposal, however, the explanatory load-bearing is carried by information destruction, vanishing rest mass, the fiat imposition of the WCH at the beginning of each cycle, and a conjectured and fine-tuned erebonic field, all of which are sustained by faith in a physics that has yet to be discovered or evidenced and is, especially in the case of mass fadeout, counter-indicated by the physics we do know. The charge that Penrose levels at others lands far more firmly on his own doorstep.
We have seen the fashion and the faith that sustains CCC. What remains is the fantasy, and this takes us to the heart of the whole proposal, the decisive question on which the entire project turns: can conformal cyclic cosmology actually accomplish the one thing it was built to do? I take up this question in the second part of this essay, which is the fourth and final installment of my discussion of cyclic cosmologies. It will be answered by addressing the model’s empirical record, its central entropy-accounting problem, and the very nature of the crossover that is claimed to join its aeons together in a beginningless eternal progression.
Notes
- To be more precise, the conformal rescaling of a spacetime rescales its metric (distance measurements) by the square of a smooth positive function. The effect is to preserve angles and causal relationships while erasing any measure of length and distinction between finite and infinite size. A conformally invariant transformation of a spacetime enables the conformal identification of two rescaled boundary surfaces as being one and the same, which allows the future infinity of an aeon that is ending to be fused to the big bang surface of its successor. What crosses this join is bare conformal structure rather than any physical metric.
- Roger Penrose, interviewed by Phil Halper, “Roger Penrose confronts creationist critic Stephen Meyer,” YouTube, 2025, https://www.youtube.com/watch?v=6YvnnPzvaJs. Penrose concedes the incompleteness of the erebon proposal at 12:53–13:25: “It needs a better theory than that. There needs a theory which explains in detail why this happens. I’m just giving you the overall picture, which is incomplete at the moment. I agree it needs more calculations. It needs [a way] to describe the erebons properly in the theory — why they decay into gravitons, into a pair of gravitons, would be the argument, and why do those gravitons survive until the next aeon, and then things are the other way around: they start to collide again and produce more erebons. So the erebons come back as the gravitons start to run into each other.”
- Penrose, Halper interview, at 16:40. At 16:37–16:55, Penrose dismisses the charge of fine-tuning outright. Responding to Meyer’s claim that CCC “has to invoke a very finely tuned amount of mass energy that will be activated at the right time and in the right way,” leaving “a huge amount of unexplained fine-tuning in his model … with no explanation for where that fine-tuning came from,” Penrose replies: “I have no idea what he’s talking about. There isn’t any fine-tuning of this sort. The main material in the universe is dark matter, and the dark matter comes about through gravitons. And it’s not a question of any fine-tuning … there isn’t any fine-tuning. I don’t know what he’s talking about.”
- Penrose, Halper interview, at roughly 19:02-19:52.