George Ellis: Why Penrose's Cyclic Universe

There's a particular kind of scientific disagreement that's more interesting than a simple clash of conclusions—it's the kind where both parties agree on the problem, admire each other's diagnosis, and then fundamentally diverge on the cure. That's what's on display in cosmologist George Ellis's recent conversation with Curt Jaimungal on the Theories of Everything podcast.

Ellis is not a critic who dismisses Roger Penrose from a distance. He co-authored The Large Scale Structure of Space-Time with Stephen Hawking, a book whose mathematical foundations owe a direct debt to Penrose's work on gravitational topology and black holes. "Roger is an incredibly creative person," Ellis says, "and his work on gravitational topological structure, gravitation and black holes was absolutely transformative." That's not throat-clearing before an attack. It's genuine, and it matters, because what follows is a serious technical objection from someone operating at the same altitude.

Where They Actually Agree

Before getting to the fracture lines, it's worth sitting with the agreements, because they're substantive.

Ellis endorses Penrose's critique of cosmic inflation—one of the most counterintuitive positions you can hold in modern cosmology, and one that often gets swamped by the mainstream consensus that inflation elegantly explains the early universe's smoothness. Ellis doesn't buy it. "Inflation is supposed to solve the problem of smoothness at the beginning. It doesn't. Inflation assumes that the universe is smooth before it ever gets going." Penrose has been making this argument for years, and it remains genuinely unresolved. The standard inflationary account doesn't explain why the initial conditions were so low-entropy—it simply relocates the mystery.

That's a meaningful concession to Penrose's instincts, and it shapes the intellectual context for what comes next.

The Infinity Problem at the Heart of CCC

Penrose's Conformal Cyclic Cosmology (CCC) is a bold attempt to dissolve the singularity problem at both ends of cosmological history. The idea, roughly: a universe that expands into a cold, dark, conformally flat far future is geometrically compatible—when you strip away scale—with a new Big Bang. Eons connect. The universe cycles, not through re-collapse, but through a kind of conformal matching at infinity.

Ellis finds it elegant in conception and broken in execution. The hinge of his argument is a point about mathematical ontology that sounds almost philosophical until you trace its physical consequences.

"Infinity is not a very large number," Ellis says. "It's bigger than any number which can possibly exist." He develops this with a disarmingly simple illustration: the universe is 13.7 billion years old. In another billion years it'll be 14.7 billion. When will it be infinitely old? "The answer is never. No matter how old it is, it's not even the first step on the road to infinity because infinity is bigger than any number that can possibly exist."

This isn't pedantry. In Penrose's conformal diagrams, you can literally see future null infinity—it's drawn right there on the page, a boundary the universe approaches. The visual representation makes it look like a place you could reach, a surface you could hand information across. But Ellis argues that treating it that way is a category error with fatal consequences for CCC.

The logic runs like this: CCC requires that signals from the end of one eon propagate through the boundary at infinity and seed the beginning of the next. But if that boundary is genuinely infinite—not "very far away" but actually infinite—then any finite signal gets diluted by an infinite factor. "The amount which gets transferred from this eon to the next is precisely zero," Ellis says flatly. "There is no way if it's actually infinite that a finite amount of information could go from this eon to that one."

In other words, the theory's mechanism—the actual transmission belt between cosmic epochs—doesn't survive contact with the mathematical object the theory itself invokes. Ellis's paper, "The Physics of Infinity," is where he develops this argument formally, and it's worth noting he isn't alone in worrying about how physicists operationalize infinity. The same slippage appears in regularization schemes in quantum field theory, in claims about eternal inflation's landscape, and in various holographic arguments—infinity gets treated as a stand-in for "very large," which is a different thing entirely.

Whether Penrose has a response to this specific version of the objection is a genuinely open question. CCC has gone through several iterations, and Penrose is not the sort of theorist who ignores pointed technical criticism. The debate about whether conformal rescaling can somehow preserve signal integrity across a true infinity is live, if not widely publicized.

ADS/CFT and the Wrong Universe Problem

Ellis extends his skepticism about infinity-dependent frameworks to AdS/CFT correspondence—the celebrated holographic duality that relates a gravitational theory in anti-de Sitter space to a conformal field theory on its boundary. He's blunt: "The trouble with AdS/CFT is it obviously doesn't describe the real universe because anti-de Sitter space has a negative cosmological constant. Now if the dark energy is a positive cosmological constant it's positive. So that by itself proves AdS/CFT doesn't apply to the real universe."

This is a known tension in the field, not an Ellis original. AdS/CFT is one of the most mathematically productive frameworks in theoretical physics, with implications for quantum gravity, black hole information, and condensed matter. But it was derived for a universe with a negative cosmological constant—a universe that curves back on itself in a particular way, with a timelike boundary you can actually reach. Our universe, with its positive cosmological constant, is de Sitter-like: it accelerates outward, its boundary is spacelike, and the correspondence doesn't obviously generalize.

Researchers have been working on de Sitter versions of holography for years, with partial results and ongoing controversy. Ellis's objection—that the sign of the cosmological constant isn't a minor technical detail—is a legitimate one, even if the community consensus is that holographic thinking remains valuable as an approximation or inspiration even outside its home turf.

His alternative framing of holography is less famous but worth understanding: the null initial value problem, developed by Ray Sachs and others in the 1970s. Data placed on a three-dimensional null cone in general relativity—a lightlike surface—mathematically determines everything in the four-dimensional interior. That's a genuine, laboratory-testable sense in which a lower-dimensional surface encodes higher-dimensional physics. No exotic dualities required, no negative cosmological constants, no strings attached. Whether it captures everything holography enthusiasts want from AdS/CFT is another matter.

What's Actually at Stake

The disagreements here aren't arcane. They're about the architecture of reality at its largest and most fundamental scales—how the universe began, whether it cycles, what it means for information to persist or perish, and whether our most powerful mathematical tools are telling us truths about this universe or a more convenient one.

Ellis's criticisms of Penrose come from a recognizable intellectual tradition: a preference for mechanisms over elegance, for mathematical objects used precisely rather than evocatively. His point about infinity isn't that Penrose is sloppy—Penrose invented the conformal diagram, after all—but that the theory may be betrayed by its own most essential tool.

Penrose has spent decades arguing that physicists are too quick to accept frameworks that work mathematically but may be physically vacuous. There's something almost recursive about an argument that says the same critique applies to CCC itself.

Whether that recursion is fatal or fixable is, genuinely, an open question. Ellis thinks it's fatal. Penrose's defenders would presumably disagree. The rest of us get to watch two of the people most qualified to have this argument actually have it—which, in the current landscape of theoretical physics, is not nothing.

By Amelia Nwofor, Science Desk Editor