This is the second of two installments on Roger Penrose’s conformal cyclic cosmology (CCC), and the last in my discussion of bouncing and cyclic cosmologies. The first CCC essay set the stage by recounting the year-long public exchange that prompted these essays, telling the story of my own academic acquaintance with Penrose, and showing how CCC ironically embodies versions of the fashion and faith Penrose diagnosed as Achilles’ heels in contemporary physics.
The fashion in Penrose’s model is his preference for a beautiful geometric structure over a physical mechanism, and, surreptitiously, an inflationary phase, doing the same work as standard inflation, smuggled into the late pre-crossover stage of the preceding aeon under another name despite Penrose’s devastating critique of inflationary cosmology. The faith evinced is in a set of load-bearing assumptions without which the model cannot function: that information is destroyed inside black holes, that rest mass eventually fades to nothing, that the low-entropy Weyl condition is legitimately reimposed at the beginning of every cycle, and that an unobserved Planck-mass particle, the erebon, supplies dark matter in the required quantity.
We are left to the consideration of the fantasy in Penrose’s conjectures, and with it the decisive question, whether CCC can do the one thing it was built to do, namely, explain the universe’s astonishingly low-entropy beginning as an inheritance passed down through an endless chain of aeons, each joined to the next by a rescaling of the geometry on their shared edge. It is to this question we now turn, and the negative answer that emerges puts the fantasy CCC embodies on full display.
Fantasy
That the constructions of conformal cyclic cosmology are fantastical is apparent right away, and the fantasy is displayed on two levels. The first level is structural. CCC asks us to accept a past- and future-eternal cycle of cosmic aeons in which matter dissipates and is reborn, each aeon joined to its predecessor and successor not by any physical transition, but by the mathematical identification of two boundaries. This crossover has no dynamics associated with it, nor any process unfolding in time; the transformation happens by the pure geometric matching of the distant-future boundary of one aeon with the beginning of the next. Whether and why such an infinite chain of universal aeons exists is a question the model passes over in silence. But the silence is thunderous, and when we listen, we find that it does not lie — there can be no such chain, let alone one with the envisaged entropic reset.
The second level is, as it should be, empirical. It is far from promising. One of the central observational predictions has been the existence of concentric low-variance circles in the cosmic microwave background (CMB), supposedly left by collisions between supermassive black holes in the previous aeon. Gurzadyan and Penrose gave the first report of such circles in 2010, but three separate independent reanalyses by Wehus and Eriksen, Moss, Scott, and Zibin, and Hajian found that these circles were entirely consistent with the standard ΛCDM model, and thus completely worthless as evidence for CCC. Not to be dissuaded, An, Meissner, Nurowski, and Penrose published a claim of a different signature in a 2018 preprint, later appearing in print in 2020 — Hawking points, rings of sharply raised temperature supposedly left by the final evaporation of black holes in the previous aeon — that was re-examined by Jow and Scott, who found it had barely more than one standard deviation of significance, but a machine-learning study in 2024 of the Planck and WMAP data showed no statistically significant signal once controls for anomalous bright and cold spots were implemented. As the Canadian astrophysicist Douglas Scott has observed, the signature predicted has migrated with each successive claim: low-variance circles were replaced by high-gradient rings. The effect is that these “predictions” were never fixed consequences of the theory, and so were never real predictions at all. Meissner and Penrose’s introduction of a new “gravitational wave epoch” in their 2025 revision of CCC, enlarging its predictions to bring them in line with the data, is a textbook example of post hoc reconciliation designed to rescue a favored theory from falsifying evidence.
The Slate That Will Not Wipe Clean
The purpose of Penrose’s model is not just to obviate the question of a universal beginning by placing it in the context of a beginningless and endless cycle, but to resolve the problem of the extraordinarily low-entropy start of each cycle represented by the smooth gravitational state that the Weyl Curvature Hypothesis (WCH) describes. Penrose wants the WCH to be a natural and automatic inheritance from the previous aeon that starts each cycle in this state of astonishingly low entropy. As the physicist’s measure of disorder in terms of the count of the microscopic arrangements that would look the same macroscopically, entropy climbs throughout each aeon, ultimately ending up in gigantic black holes as the highest-entropy objects in the universe. If this disorder carried over from cycle to cycle, there would be no reset, and this is the problem Penrose must address.
Penrose’s attempt to resolve it has two crucial elements. First, all of these black holes, over a finite stretch of time that boggles the imagination, will eventually evaporate as their mass bleeds away in Hawking radiation. This yields a far future in which the geometry is exceedingly smooth again and gravitational disorder has fallen back toward zero. All of this, which involves the coarse-grained thermodynamic entropy of the universe governed by the Second Law, is relatively uncontroversial. But there remains the fine-grained quantum-mechanical von Neumann entropy that, because of the unitary evolution of the wavefunction, remains constant over time. Unitarity conserves information about quantum states, so a state that begins pure remains pure. If quantum mechanics holds, then the total system of the black hole and its radiation must remain pure and its information must be conserved, even when it evaporates. For this information to be preserved, the entropy of the Hawking radiation must reach a maximum and then fall back to zero as the hole evaporates, following what is now called the Page curve, which tracks the fine-grained entanglement entropy of the radiation rather than its coarse-grained thermodynamic entropy. Recent work in quantum gravity strongly supports this requirement and the prevailing view is that this is what happens. But this is not what Penrose needs, and so we arrive at the second element in his attempt to resolve the entropy problem, the load-bearing claim that black hole evaporation genuinely destroys information. The tally of disorder really disappears rather than just being shifted from one place to another. And so, Penrose claims (2018: 1183), “the 2nd Law is not violated; it is transcended in the sense that the effective entropy definition has to shift down to that which is relevant to the new aeon.” Two distinct ledgers are in play, and the distinction is decisive: black hole evaporation returns the gravitational (Weyl) entropy to zero, but the thermodynamic entropy of the radiation it sheds is the separate quantity that crosses over.
I examine this load-bearing claim in a paper currently in preparation, showing it is false after making the requisite quantitative calculations — the entropy reset that Penrose needs cannot happen.1 If we add up the current disorder of the observable universe, we find that the figure is staggering and almost all of it resides in supermassive black holes. The entropy of the Big Bang, on the other hand, was approximately fifteen orders of magnitude — a thousand trillion times — smaller. The critical issue for CCC is that it must make this gap disappear at the crossover, and it cannot do so.
There are two reasons that CCC cannot reset the entropy, neither of which relies on exotic physics. The first is that as a black hole evaporates, its disorder is not annihilated but radiated to the exterior as the hole gradually disappears. The eventual disappearance of the black hole itself does not remove the entropy already in the external radiation field. In fact, a careful accounting shows that the radiation carries slightly more entropy than the black hole itself, not less. While the geometry of the universe becomes smooth because the black holes that warped it have been removed, the disorder they contained has merely shifted address, passing from the black hole’s gravitational field into an amorphous ocean of dim light and gravitational waves that fills what once was the observable universe. The second reason poses the fundamental problem for CCC: conformal rescaling cannot touch the disorder present in this amorphous ocean. Its statistical entropy, a pure number consisting in a plain count of arrangements, cannot be altered by a change of scale. The radiation bearing this disorder is massless and left untouched, which it must be in order for the conformal invariance that Penrose needs to hold. The irony is that the very scale-insensitivity that Penrose requires to be able to stitch one aeon to the next is the condition rendering the rescaling impotent to lower the statistical entropy of the radiation that crosses over. The big bang of the next aeon thus inherits an entire fifteen orders of magnitude more entropy than is permitted by a universe with a beginning like ours.
But this is not the whole of it. The situation is made worse by the dark-energy expansion at the tail end of the previous aeon that, Penrose concedes, plays the same role that standard inflation was invented to play after the big bang. This concession carries with it the same problem for the crossover that Penrose has long noted for standard inflationary cosmology. As the smoothing effect of dark energy grows with the disappearance of matter in his model, the accelerating expansion is an entropy-raising process affecting the final stages of an aeon when the entropy is meant to fall to zero. One might further argue that the associated de Sitter horizon entropy is enormous, larger than any the black holes ever held. Penrose’s accounting would not include horizon entropy, however, because (1) gravitational entropy is measured by the Weyl curvature that vanishes in the far-future conformally flat de Sitter space; (2) it hides no in-fallen degrees of freedom like a black hole; and (3) it is observer-dependent. While this exclusion is contestable since Gibbons-Hawking and other standard accounting treat the horizon term as real and dominant, my argument has no need of it. All that matters for our purposes is the radiation entropy that black hole evaporation releases into the matter sector, and this is untouched by Penrose’s reasons for setting horizon entropy aside.
One might think that there is a key element of CCC that could address and lower this entropy balance, viz., the destruction of information offered as an article of faith that I discussed in my last essay, and that we encountered again a few paragraphs ago. One would be wrong to think so. First, as already noted, it runs against the grain of the best work on evaporating black holes, which preserves the unitary evolution of quantum systems and shows how information can be conserved. Betting on information loss is not a safe assumption, and if one tries to build a version of CCC that conserves it, one winds up no further ahead. Eckstein (2023) has built a version of CCC that preserves information and resets the gravitational entropy, but it contains no basis for removing the radiation entropy that a unitary crossover also keeps intact. The only way to remove it is by a fine-tuned fiat that imposes the low-entropy condition by hand when it glues the aeons together at the asserted crossover. The point is that even if we grant Penrose his information loss in the strongest form, it addresses the wrong question. There are two things going by the name of entropy here — one is a fine-grained measure of how much of the past could, in principle, be reconstructed; the other is the coarse-grained thermodynamic disorder of the radiation at crossover. Destroying information would lower the first but it leaves the second untouched. Even if black hole evaporation destroys the information that has fallen inside the hole, what the next aeon inherits is already outside the black hole as radiation it dispersed through space before it vanished. Eckstein’s remedy reaches into the wrong place for the wrong quantity.
The bottom line is that the low-entropy beginning is not produced by any of the physical mechanisms in view, nor is it produced by the mathematical identification that constitutes the reset. It is put in by fiat as the assumed smoothness of the crossover surface in the form of the Weyl Curvature Hypothesis as an unevidenced article of blind faith. CCC does not dissolve the deepest fine-tuning in cosmology; rather, it reimposes it with every crossover. This is exactly what the other cyclic and bouncing models were found to do in the first two installments of this series. And, of course, this leads down a familiar path. If co-moving entropy is non-decreasing, then disorder can only climb from cycle to cycle. At most one big bang sits at the low-entropy floor demanded by the WCH, with every later cycle farther above it, in violation of the very condition the model was invented to secure. Conformal cyclic cosmology thus furnishes its own reductio instead of the beginningless succession of resets it was meant to supply. Penrose has not “transcended” the Second Law; he has declined to count the disorder still there and accumulating with each cycle, which is no explanation at all of our universe’s low-entropy past.
The Crossover Cannot Bear the Weight
But suppose we ignore all of these difficulties. It is still the case that CCC would fail as an explanation of our universe, and the reason for this takes us back to the conformal maneuver on which the model is predicated.
While each aeon is past-incomplete, it does not constitute an absolute beginning in Penrose’s model because the crossover uses conformal rescaling to identify each aeon’s big bang with the far-future boundary of its predecessor. This conformal rescaling is an identification between mathematical descriptions; it is not a causal process or physical continuation of any kind. Penrose grants this, describing the join between aeons as “a smooth transition, but only in a conformal geometry,” and stating “there’s no metric which carries you across.”2 This is precisely the problem, acknowledged in Penrose’s own words. Where there is no metric, there is no physical passage, only a mathematical matching of two scale-free descriptions. The actual physical structure of the far future of one aeon and of the big bang of the next aeon remains in place. These are utterly different physical states and to equate them simply because their scale-free descriptions coincide is to confuse what the world contains with what a formalism can express. As Steve Meyer remarked in his discussion of Penrose’s model with Sean McDowell, declaring Mount Everest to be “one mountaineering unit” tall does nothing to shorten the climb.3 All that has changed is the ruler, not the mountain. Changing how we measure the size and energy of our universe changes neither its size nor its energy, but CCC requires the actual change of these things, something a mere mathematical redescription could never do.
One is not free to reply on Penrose’s behalf that the model does without classical thermodynamics and fixed particle masses, so the mathematical rescaling is legitimate and does not run afoul of physical constraints. This gets the situation precisely backwards. The reason the model abandoned these things was so that it could conformally rescale. The abandonment isn’t a discovery about nature; it’s a stipulation required by the model that has no independent justification. Neither can one reply by saying that the postulated crossover isn’t an energetic process because it’s topological and orientational, so no thermodynamic laws are broken. This is just a restatement of the fundamental problem at issue — mere mathematical descriptions that are equivalent in a specialized sense, but blind to a physical change that must take place, provide no basis for asserting that the needed physical change either has happened or can happen.
The situation only gets worse. The Tod equations for CCC underdetermine the conformal factor at crossover, instead admitting a whole family of solutions. Choosing which solution is best requires information that the equation itself does not supply. Different principles for making this choice have been proposed by Newman, Nurowski, and Tod, none of which agree with Penrose’s original assumptions. A review of this state of affairs in 2022 by Markwell and Stevens maintains that the arbitrariness of this choice presents an obstacle to the coherence of CCC that remains unresolved. The central equation on which the whole cosmology rests is thus both causally inert and ill-defined, an arbitrary choice among different descriptions, none of which describe a physical process that does anything.
When the masks come off at the conformal masquerade ball, the endless cycle of aeons is revealed to be one — there is no crossing, there is only our universe, and it has a beginning. Much like the Bars-Steinhardt-Turok (BST) model, the promise of CCC rests on a conformal symmetry that nature itself does not possess, and is bought by sacrificing the constancy of rest mass, which is either driven to the Planck scale at a BST “bounce,” or faded to nothing in the remote future by Penrose. It is no coincidence that the Planck-scale mass BST forces on ordinary matter at the crunch is the very same mass Penrose reserves for his hypothetical erebons. Two models that look quite different on the surface share the same deep structure and strategy. They both retreat into a mathematical description that is blind to scale and incapable of registering an ultimate beginning, then report, having hidden it behind a conformal transformation with no physical significance, that there is no beginning to be found. BST and CCC thus offer variations on the same deceptive theme, but when the curtain is pulled back after the overture has been played, what is revealed is not the grandeur of the universe, but a tiny collection of physicists building mathematical castles in the air.
Where We Stand
We have journeyed through essays on the BGV theorem and efforts to avoid its implications of past-incompleteness by exploring the resources of cyclic, bouncing, and asymptotic cosmologies. It is worth speaking plainly now about what has been discovered and what has not. One thing that has not been discovered is a formal mathematical proof of a cosmic beginning, but we have neither been seeking nor asking for this kind of deductive certainty. As Steve Meyer has made clear on multiple occasions, and I am making clear again now, the argument here is abductive, not deductive. It is a matter of what is the best explanation for the universe in which we find ourselves.
But this concession still leaves a powerful logical “trilemma” that is quite worth stating: either the universe began, in which case its beginning requires a cause that lies beyond space, time, matter, and energy; or our universe is part of some larger reality that is past-eternal, the models for which involve unexplained and extraordinary fine-tuning that implies an intelligent cause; or, to exhaust the options, whether temporally finite or eternally existing, the reality of our universe is a brute fact that is the way that it is for no reason at all. As the cosmologist Edward Tryon once put it, “our Universe is simply one of those things which happen from time to time.” And down this last path lies madness and the end of science. If whole universes can happen for no reason at all, so can anything in those universes. The simplest hypothesis is that a single consciousness (our own) popped into existence for no reason at all, has the thoughts it is currently having for no reason at all, and the universe itself is nothing more than the phantom dream of an inexplicably conscious Boltzmann brain.
Penrose was right, then, that fashion, faith, and fantasy have led much of modern cosmology astray. He was more right than he knew, for these same three forces have beguiled his own efforts. A century of strenuous effort by the finest minds in physics has left as the best explanation the one with which it began: a universe with a beginning in the finite past; the absence of any tenable, self-sufficient, physical explanation for what stands behind it; and the seemingly ineluctable need for a self-existent, transcendent intelligent cause to make sense of any of it.
Notes
- I develop this quantitative argument in my paper “The Entropy Budget of a Conformal Crossover” (in preparation). The paper assembles the entropy ledger of a single aeon from the Bekenstein–Hawking entropy of black holes, the supermassive-black-hole census of Egan and Lineweaver (2009), and the Hawking evaporation timescales, addressing the technical objections in full.
- Roger Penrose, interviewed by Phil Halper, “Roger Penrose confronts creationist critic Stephen Meyer,” YouTube, 2025, https://www.youtube.com/watch?v=6YvnnPzvaJs. Penrose makes this statement at about 10:36-10:44.
- Stephen Meyer, interviewed by Sean McDowell, “At What Cost? Stephen Meyer Assesses the Conformal Cyclic Cosmology of Sir Roger Penrose,” https://www.youtube.com/watch?v=Na-JhfN4Q94 . Meyer makes this point as part of his critique in his remarks from 29:25-31:00.