The rumblings and grumblings continue apace, some based on misunderstandings of Steve Meyer’s argument in The Return of the God Hypothesis, The Story of Everything film, and his debate with Phil Halper on Justin Brierley’s podcast, and others rooted in confusions about the implications of various cosmological theories themselves.
A prevalent misunderstanding, evinced in a video made by Halper after the debate was filmed, is that Steve’s whole argument rests on the idea that there’s a singularity constituting the absolute beginning for everything that exists. This is a caricature. While it’s true that singularity theorems and the Borde-Guth-Vilenkin (BGV) theorem play a role in his case for intelligent design, Steve’s arguments draw on multiple lines of evidence, asking which metaphysical foundation, theism or naturalism, provides the best explanation for everything science has revealed about the universe we inhabit. The form of the argument he relies on is abductive, not deductive. The big picture, considering multiple streams of evidence, is that theism provides a consistently better and vastly more defensible explanation for the way things are than naturalism, regardless of which cosmological model one favors. But making this case requires working through all the evidence and all the different models in a systematic way.
As I was wrapping up this essay, my colleague David Klinghoffer drew my attention to a recent review by astrophysicist Emma Chapman of Halper’s co-authored book in the Wall Street Journal. Two sentences in the review state Halper’s position briefly and clearly. Chapman describes the position by saying, “Observations of the cosmic radiation background provide nearly incontrovertible proof of the big bang. But the conviction that the universe began as an infinitely dense point in spacetime is now less certain.” This summary is accurate and it’s important to note that the doubt it expresses focuses on the initial singularity, not on a beginning as such. As we shall see, the beginning of the universe doesn’t need to be singular, so doubts about a singularity don’t need to translate into doubts about a beginning. And Steve’s argument, being abductive, doesn’t rest on a singular beginning anyway.
The other concern I mentioned, confusion over the implications of various theories and results in cosmology, is what will occupy us in this series of essays. Most particularly, I want to address confusion over the scope and significance of various singularity theorems and of the BGV theorem. These issues dominate Halper’s post-debate video aiming to “debunk ID guru Stephen Meyer,” and they are a recurring subject of emails inundating the inboxes of various Discovery Institute fellows. Because the territory is large, I will take it in several installments. This first one concerns bouncing and cyclic cosmologies in general, together with the theorems that bracket them; a second takes up loop quantum cosmology; and the last two focus on Penrose’s conformal cyclic cosmology.
Let’s start by talking about the Borde-Guth-Vilenkin (BGV) theorem, which, after earlier iterations and tweaks, received the final form of its proof in 2003. Stated precisely, the theorem shows that if the average rate of cosmic expansion is positive along any past-directed geodesic, then that geodesic is past-incomplete (cannot be extended to arbitrary earlier times). In a universe like ours, this condition holds along almost every observer or photon worldline. This result is purely kinematic and depends only on the geometry of expansion, not on any energy conditions. Since the theorem does not mandate that every geodesic be past-incomplete, every attempt to avoid past-incompleteness begins with trying to exploit this fact.
As we shall see, however, the room for maneuverability is very limited and its plausibility is highly suspect. The go-to strategy for circumventing the theorem has been the invention of bouncing or cyclic cosmologies of various sorts. We will consider several here and show that either they do not work or are exceedingly implausible. In the case of a genuine bounce, the idea is that geodesics might extend through it indefinitely, allowing the universe to be past-eternal. But extending this through infinitely many cycles without running into entropy problems requires a net expansion of the universe across cycles, which is precisely the condition the BGV theorem needs to prove past-incompleteness. Bounces alone cannot avoid a finite past. Let’s take a closer look at why various and sundry evasion strategies do not work.
Old and New Cyclic Models
The original cyclic ekpyrotic model, developed within string cosmology, was proposed by Paul Steinhardt and Neil Turok in 2002. The picture it offers is of multiple big bangs happening when two parallel three-dimensional “branes” separated by a small extra spatial dimension collide in higher-dimensional space as part of an endless cycle of collision and separation. Each cycle has a long dark-energy expansion phase that dilutes the entropy density that would otherwise accumulate, thus addressing the entropy-accumulation problem that Richard Tolman identified in 1931, namely that cyclical models eventuated in a thermal soup incapable of supporting structure after multiple iterations. Resolving the Tolman entropy problem with net expansion over cycles, however, made the Steinhardt-Turok model subject to the BGV theorem and past geodesic incompleteness.
To avoid the extra theoretical baggage of string cosmology and branes, the newer Ijjas-Steinhardt cyclic model addresses the Tolman entropy problem using four-dimensional general relativity with a scalar field driving the dynamics. In this context, the bounce is a smooth, nonsingular event with no branes or extra dimensions. The Hubble parameter, which measures the rate at which the universe expands or contracts, oscillates between expansion and contraction, while the scale factor, which measures the overall size of the universe, grows exponentially across cycles. This net growth, despite oscillation, handles the problem of entropy inherited from previous cycles. Ijjas and Steinhardt develop this model in two papers, “A new kind of cyclic universe” (2019) and “Entropy, black holes, and the new cyclic universe” (2021), and argue that it solves the Tolman entropy problem, opening the door to a universe that is eternal into the past. But it doesn’t. The exponential growth of the scale factor across cycles yields a positive averaged Hubble parameter, which is all that is needed for BGV to demonstrate past-incompleteness.
The Kinney-Stein Result
The fact that the Ijjas-Steinhardt model is subject to the BGV theorem was proved in 2022 by William Kinney and Nina Stein. They showed directly that the same cycle-to-cycle growth of the scale factor that enables the model to dissipate entropy produces the positive averaged Hubble parameter that guarantees past geodesic incompleteness.1 No bouncing model dissipating entropy through growth of the scale factor can truly be cyclic in time, but abandoning cycle-to-cycle growth reinstates the Tolman entropy problem. Bouncing cosmologies must pick their poison.
Wall’s Quantum Singularity Theorem
There is another thermodynamic result that complements BGV arguments by closing a loophole often used by bounce cosmologists. At a bounce, negative energy densities occur as a quantum effect that violates the classical energy conditions on which the classical singularity theorems of Penrose (1965) and of Hawking and Penrose (1970) depend. In violating the classical requirement that matter always has positive energy, localized negative energy densities create repulsive gravity that allows the universe to rebound without collapsing to a singularity. What Aron Wall showed in his proof of the Generalized Second Law (GSL), using the Bekenstein-Hawking result that a black hole’s horizon area is proportional to its entropy, is that even when the semi-classical effects of volatile quantum field fluctuations and negative energy densities are taken into account,2 the combined entropy of matter and of a causal horizon must always increase. Wall further proved that the GSL itself entails a quantum singularity theorem that does not rely on classical energy conditions. What Wall’s theorem shows is that spatially infinite Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies, of which ours appears to be one, are past geodesically incomplete. This rules out the possibility of independent baby universes and of restarting inflation, both of which are common bounce-cosmology strategies. The end-run around classical energy conditions due to quantum effects has been foreclosed since Wall’s theorem replaces those energy conditions with the GSL, which already accounts for those effects. The BGV theorem thus constrains bouncing cosmologies kinematically while Wall’s theorem constrains them thermodynamically.
Six Evasion Strategies in the Literature
Needless to say, advocates of bouncing cyclic models want to evade this conclusion. Turning to the literature, we find six main strategies attempting to do so. We will define the relevant terms as we consider each case, but for now we merely list them. Four of these strategies postulate some kind of asymptotic past state from which the universe is supposed to have emerged: (1) the emergent universe, in which the asymptotic past is an Einstein static state; (2) the Aguirre-Gratton model, in which the asymptotic past is a flat-slicing of de Sitter space with a time-symmetric null boundary; (3) the Ijjas-Steinhardt model, in which the asymptotic past is a Minkowski-like initial state followed by a long phase of slow contraction; and (4) the Carroll-Chen model, in which the asymptotic past is a near-Minkowski de Sitter substrate from which inflation arises spontaneously. To these four strategies two different approaches are added: (5) a highly selective conformal frame change that defines a beginning out of existence; and (6) positivistic assertions of ontological deflation because of observational underdetermination (indistinguishability). Let’s deal with these in turn.
The Emergent Universe
George Ellis, first with Roy Maartens, then further developing the model with Jeff Murugan and Christos Tsagas, proposed that the universe approaches an Einstein static state asymptotically in the infinite past (Ellis and Maartens 2004; Ellis, Murugan, and Tsagas 2004). An Einstein static state, so-called because it matches the configuration Einstein used in 1917 to yield a static cosmological solution to his field equations, precisely balances matter density and a small positive cosmological constant to preserve a closed, positively-curved 3-sphere geometry of constant size. In the Ellis-Maartens model, a scalar field (having magnitude but no direction at each point) with a very carefully chosen “plateau” where its potential energy density is extraordinarily flat, preserves the classical stability of its static state against small perturbations. This scalar field eventually rolls off the plateau, which destabilizes equilibrium and triggers an inflationary phase that gives way to the standard hot Big Bang scenario. Since the Hubble parameter is exactly zero through the infinitely-old asymptotic Einstein static phase, the average expansion rate over past-directed geodesics is also zero, avoiding the conditions of the BGV theorem.
Unsurprisingly, the viability of past-eternality fails in the model for quantum-mechanical reasons. As Audrey Mithani and Alexander Vilenkin have shown (2011, 2012), even though the Einstein static state is classically stable in the Ellis-Maartens model, it is quantum-mechanically unstable, so there is a non-zero probability per unit time that the universe will tunnel to zero size. Three conditions that the Einstein static state satisfies must hold for the Mithani-Vilenkin argument to work: first, the universe must rest in a classically stable configuration akin to that of a marble at rest in a bowl; second, there must be a barrier between that configuration and a state of zero size that functions like the sides of a bowl; and third, the universe must be localized sufficiently for a standard tunneling calculation to be tractable. This is enough to show that the asymptotic Einstein static past cannot be infinitely old since, over an infinite past, this tunneling would already have happened with probability one. The model does not, therefore, give us a beginningless cosmology because the universe could not have sat in this static state forever. The universe had a beginning.
An Asymptotically de Sitter Past
Anthony Aguirre and Steven Gratton have proposed a model in which our universe might be one half of two branches, each an asymptotically inflating de Sitter region (i.e., devoid of mass and radiation energy and having positive vacuum energy) joined together by a null hypersurface (light-ray path) that is a boundary at which time reverses (“Inflation without a Beginning,” 2003). There is no singular big bang here since each branch expands into its own distinct future from the boundary, and observers in a given branch see their past-directed geodesics cross the boundary into a contracting de Sitter region, so the average Hubble parameter along the full geodesic vanishes and the BGV theorem is avoided. Vilenkin has shown (“Arrows of Time and the Beginning of the Universe,” 2013), however, that the boundary surface itself functions as an effective beginning since the past for observers in one branch cannot operationally be extended into the other, nor can either side reconstruct the matter content and physical history of the other. That the universe began to exist does not require the past boundary to be singular rather than a null hypersurface in de Sitter space. A universe emerging from a null hypersurface like this just has a beginning of a different sort, with the same metaphysical implications. Beyond this, the Aguirre-Gratton construction has the standard measure problem and Boltzmann brain pathologies of eternal de Sitter inflation (Dyson, Kleban, and Susskind, “Disturbing Implications of a Cosmological Constant,” 2002).
It also is worth noting that while the Aguirre-Gratton model does not satisfy the conditions for the Mithani-Vilenkin tunneling argument since it is rolling outward from its central boundary in opposite temporal directions and there is no tunneling probability to compute, a generalized version of the quantum instability argument does still apply. The boundary surface requires highly fine-tuned, low-entropy initial conditions on the precisely constructed hypersurface for both branches in order for them to join smoothly in the requisite way, and quantum fluctuations of this fine-tuning have non-zero amplitude per unit of time. If the past were infinite, these fluctuations would have disrupted the precise boundary conditions required by the model an infinitely long time ago. Understood as a general principle, quantum instability, which defeats the past-eternality of emergent universe models, also defeats past-eternality in the Aguirre-Gratton scenario. A different structural pathway leads to the same conclusion, reinforcing Vilenkin’s point that the boundary surface itself is an effective beginning.
Slow Contraction from a Minkowski-Like Past
Paul Steinhardt and Anna Ijjas, along with several collaborators, have constructed a model that avoids a big bang singularity and the conditions of the BGV theorem (Ijjas et al. 2020, 2021, 2024). In this model, the universe arises from a generic, very low-curvature state that approximates Minkowski space, after which an ekpyrotic scalar field produces a long phase of slow contraction. This field is given an ultra-stiff equation of state, which means the ratio of its pressure to energy density greatly exceeds 1, a range it reaches by rolling down a precipitous negative potential while gathering tremendous kinetic energy. To put this in perspective, ordinary matter’s pressure-to-energy-density ratio is 0, that of radiation is 1/3, and the cosmological constant’s is -1. During the contractive phase, the energy density of the ekpyrotic field dominates everything else. Numerical simulations confirm that this contraction has the effect of smoothing and flattening generic starting configurations, yielding the homogeneous, isotropic, and spatially flat universe required for a bounce into the expanding phase of a universe like ours. As Steinhardt and Ijjas et al. intended, the model straightforwardly evades the BGV theorem because the Hubble parameter is negative during the contraction phase, making the expansion rate along past-directed geodesics non-positive so that the conditions for the BGV theorem are not satisfied. In this regard, note that the model’s claim to past-eternity rests on the asymptotic Minkowski state, not on any bounce structure that might be built on top of it. Any cyclic version of the model has finitely many bounces between the Minkowski past and the present, so the initial Minkowski-like state is doing all the work for BGV evasion.
Two objections along with a more fundamental concern undermine the model as a sufficient account of a beginningless cosmos. The first is that the postulated Minkowski-like initial state with its invented ekpyrotic scalar field is an extraordinarily special, low-entropy construction with observationally unprecedented properties. If the initial state were genuinely generic, it would have high entropy and great disorder, which is the opposite of what the model needs for its smoothing phase to function. The asymptotic Minkowski past with a special ekpyrotic scalar field is highly fine-tuned and not a natural starting condition. All of these things demand an explanation before they could ever function as one. One cannot just help oneself to the existence of radically contingent fine-tuned entities deliberately invented to obviate an explanatory demand when those entities are just as much in need of explanation. The second problem is that any cyclic extension of the model, unless one supposes without justification or mechanism that entropy dissipates at each bounce, runs into a thermodynamic dilemma. Either entropy must accumulate and increase across cycles, in which case Tolman heat death results and an infinite past series of bounces is precluded, or the entropy is dispersed by volume growth in the scale factor, which leads to an average positive Hubble parameter, meaning that the BGV theorem regains traction via the Kinney-Stein result. Either way, the universe cannot be past-eternal in its cyclic history.
Finally, a deeper quantum-theoretic concern parallel to the Mithani-Vilenkin argument defeating the emergent universe can be raised. The conditions of the Ijjas-Steinhardt model are different, so the Mithani-Vilenkin critique does not apply, but a generalized version of the argument does. In order for the ekpyrotic scalar field to drive contraction, its asymptotic configuration cannot be completely stable at the bottom of its potential. If it were, it would never begin to roll and the contraction would never start. The field must therefore be in some metastable configuration that contains the seed of its eventual evolution. Quantum physics gives this configuration a non-zero amplitude to fluctuate per unit of time. If the past were infinite, these fluctuations would have triggered the contraction an infinitely long time ago, so the near-Minkowski state with its ekpyrotic field could not have existed to past infinity. The Ijjas-Steinhardt model’s Minkowski-like initial state must therefore have a beginning, since it must give rise to the contraction in finite time that leads to the universe-generating bounce. In short, the Ijjas-Steinhardt universe has a beginning, however hard it tries to avoid one.
The Carroll-Chen Spontaneous Inflation Model
Sean Carroll and Jennifer Chen propose a different gravitational model for cosmological origins (Carroll and Chen 2004, 2005). They propose a spatially infinite near-Minkowski (flat) space with infinitesimal positive vacuum energy as the substrate for their construction. Within this substrate, they postulate there is a unique spacelike slice of lowest entropy (a “minimal-entropy Cauchy surface”) that serves as a central slice anchoring their model. On either side of this slice, the entropy increases outward and points to the future, whereas the direction back to the slice points to the past. If the arrow of time is defined by increasing entropy, then time is reversed globally for motion away from the slice on one side relative to the other. The cosmos is thus temporally symmetric about this central slice. Throughout the substrate there is a very low Gibbons-Hawking temperature (the de Sitter analogue of Hawking radiation emitted by black hole horizons) that is the source of thermal fluctuations in an inflaton field. It follows that with low but non-zero probability, random fluctuations of the inflaton field to large values in small patches of the substrate trigger inflation and generate baby universes throughout global spacetime, with each baby universe having its own local thermodynamic arrow of time. These local arrows align with the global arrow on whichever side of the central slice they find themselves, so the picture is of an infinite substrate with no global beginning or end, containing infinitely many baby universes, each having a local arrow of time inherited from the global arrow on its half of the substrate. From either side of the central slice, the past seems to extend back indefinitely, and the BGV theorem does not apply because the substrate itself effectively has a zero average expansion rate.
Three serious objections immediately present themselves. The first is that Vilenkin’s analysis (“Arrows of Time and the Beginning of the Universe,” 2013) presents the model with a dilemma. If the substrate is non-singular, then the (null convergence) condition governing the model dictates that the Cauchy surface between the two regions must be compact and cannot extend to infinity in any direction. The spacetime of the substrate is then similar to the two-branch Aguirre-Gratton construction and inherits all of its difficulties, including the quantum instability that precludes an infinite past. On the other hand, if cosmological singularities are permitted, the infinite Cauchy surface in the Carroll-Chen model will yield inflating regions in opposite time directions that are either surrounded by singularities or have singularities in their past or future. Either way, the Carroll-Chen model doesn’t deliver the unbounded, past-eternal spacetime that motivated its construction. Second, the ground state that Carroll and Chen postulate as “natural,” namely infinite empty space with an infinitesimal positive vacuum energy, is itself, much like the Steinhardt-Ijjas et al. proposal, a highly specific condition that requires an explanation rather than supplying one. Again, one cannot just help oneself to the existence of a radically contingent entity deliberately invented to obviate an explanatory demand when that entity is just as much in need of explanation. The third and final objection is the “measure problem” and the so-called “Boltzmann brain paradox.” The occurrence of every event infinitely many times renders probability assignments ill-defined, and prediction intractable, and, in an infinite universe with quantum fluctuations, the overwhelming majority of observers, if they are such, are momentary thermal fluctuations into disembodied brains rather than into baby universes eventually leading to observers like us. Any model that produces a cosmos with these properties epistemically undermines itself (Dyson, Kleban, and Susskind, “Disturbing Implications of a Cosmological Constant,” 2002). For this objection to have full force requires identifying minds with brain-shaped matter configurations, a strong materialist assumption. Without this assumption, the fleeting thermal fluctuations are brain-shaped arrangements of mere matter, a different but weaker claim. Ironically, then, the objection hits hardest against the very materialist assumptions that drive these kinds of cosmological speculations.
As a concluding observation, we note that the last of the three objections shows how the Carroll-Chen model succumbs to consequences of the generalized quantum instability principle (directly through Boltzmann brain dominance and relatedly through the measure problem) in a different way than this principle defeats the Ellis-Maartens, Aguirre-Gratton, and Ijjas-Steinhardt models. The Mithani-Vilenkin version of the principle defeats emergent universe models, and the generalized quantum instability principle structurally defeats the asymptotic de Sitter and slow contraction models in a similar way, showing they could not be past-eternal. In the case of the Carroll-Chen model, however, the question is not whether the substrate can persist to past-eternity—the model structurally allows it, though the first two objections come into play to challenge the cogency of the hypothesis—rather, the problem is that the quantum instability the model relies upon to nucleate inflationary patches leads to a Boltzmann brain dominance that epistemically defeats the model’s claim to have established the possibility of past-eternity (or the rational warrant for any other conclusion drawn from within the model).
Changing Conformal Frames
If the goal is to get rid of a beginning to the universe, what should we make of an approach that redescribes its history in different units that make the beginning disappear? Stated roughly, this is the general strategy of Itzhak Bars, Paul Steinhardt, and Neil Turok (Cyclic Cosmology, Conformal Symmetry and the Metastability of the Higgs, 2013). To this end, they use a reformulation of general relativity with two peculiar features. First, the masses of particles are not fixed, but rather conferred by the Higgs field. Second, by using the freedom introduced by choice of conformal frame, the units for measuring both length and time can be stretched or shrunk from one place to another without changing any physical predictions.3 By exploiting the possibilities of a carefully chosen conformal frame, a cycle-ending bounce that would have been an edge of spacetime where a worldline stops in ordinary units gets rescaled so that particle masses climb toward the Planck scale where the universe grows small, and a worldline can be drawn straight through it. There are thus no past-incomplete geodesics, so Bars, Steinhardt, and Turok (BST) claim to have modeled a cyclic universe without a beginning.
There are two very heavy costs incurred by this approach. The first is its use of exotic and wholly unobserved physics. The way that one cycle is joined to the next requires a short interval between big crunch and big bang when the quantity that sets the strength of gravity (which is variable in their theory) changes sign. In other words, gravity reverses. BST rightly call this an “antigravity” phase, and there is simply nothing in established physics that asks for such a thing.
The second cost is even more serious. We can get at it by asking what the rescaling really accomplishes. The authors present their elevation of conformal symmetry to a fundamental gauge symmetry as motivated by scale symmetries in particle physics and cosmology, but none of these remotely license what they do or the conclusions drawn from it. The symmetries they invoke are approximate and global, whereas what they install is a local, exact gauge symmetry. One might initially think they’re entitled to their approach because, within their reformulation, different conformal frames are genuinely equivalent, just choices of units, so they are not tendentiously choosing one in which the bounce looks smooth. The problem is that the freedom to rescale is not a symmetry discovered in nature. It is actively put into the reformulation by the addition of an extra field whose sole purpose is to carry the absolute scales that are fixed in ordinary physics. BST freely admit that if this added field is held constant, fixing the units once and for all, their theory collapses back to ordinary general relativity, with a real curvature singularity at the crunch, and the BGV theorem in full effect. The conformal freedom on which their escape from a beginning depends is something they have manufactured, not something found in nature. To adopt deliberately a description that erases a past boundary and then conclude that there isn’t one is to sell as a “discovery” what was only ever a choice of units.
Another significant problem is that conformal rescaling does not address thermodynamics. While the conformal transformation aims to make all past-directed geodesics complete, it does nothing to alleviate the accumulation of entropy every cycle. The only way BST can avoid the accumulation of entropy leading to Tolman heat death is to invoke a net expansion over cycles that sufficiently dilutes the entropy deposited during each cycle. But this net expansion across cycles yields a positive averaged Hubble rate that the Kinney-Stein proof shows to meet the condition of the BGV theorem and entail past-incompleteness. This cannot be evaded by changing the conformal frame because the total entropy of a comoving region is set by counting microstates, which yields a pure number that no rescaling of length or mass can alter, even though the entropy density can be made to look bounded because it divides the total entropy by a frame-dependent volume.4 Furthermore, entropy does not decrease at the bounce. But such a decrease is exactly the loophole that Wall’s generalized second law closes because it covers the quantum negative-energy regime in which a bounce takes place. Working backward, a count that climbs with every cycle and cannot fall below zero allows for only finitely many cycles, so it doesn’t matter which conformal frame is chosen because the universe has a beginning in every frame.
A final, equally deep problem remains. Conformal frame changes are the wrong instruments for investigating whether the universe actually had a beginning (as opposed, perhaps, to trying to obfuscate the matter). At its root, the question of whether the universe had a beginning is settled by facts about the scale of proper time along worldlines and about whether the curvature of spacetime heads to infinity. In contrast, by design, a change of conformal frame is blind to scale. Conformal transformations preserve angle and causal relationships while discarding all measures of length, so beginnings are precisely the kind of feature that can be obscured. To deliberately move into a conformal frame where the beginning is invisible and then announce that there is none conflates the limitations of the description with features of the world. We will meet the very same maneuver, albeit in a different conformal costume, when we consider Penrose’s conformal cyclic cosmology (CCC) in the final two installments of our analysis of cyclic cosmologies. In CCC, another conformal symmetry that physics does not actually possess is again constructed for the purpose of redescribing away a past boundary. Unsurprisingly, rest mass is a casualty in CCC too, though Penrose has it fading away in the far-distant future, whereas BST drive it to the Planck scale at the bounce (the very Planck-scale mass Penrose reserves for his hypothetical “erebons”). While the two models use conformal rescaling in different ways and differ in a lot of the mathematical machinery they invoke, their strategies are the same. They both erase a metrical beginning by taking refuge in a mathematical description in which metrical beginnings have no place. A cyclic bounce model and a bounce-free cyclic model that only work by putting to death the constancy of mass and mathematically banishing metrical beginnings are pied pipers playing very beguiling tunes. We should be wary of being led into a trap.
Observational Underdetermination
When physics fails to generate the solution you want, there is always the fallback offered by bad philosophy. One might grant that no cyclic constructions, whether they succeed in evading the BGV theorem or not, ultimately provide a plausible scenario that avoids a universal beginning, but still argue that since it is impossible to distinguish observationally between a genuinely past-eternal cyclic universe and an emergent one followed by an arbitrary finite number of cycles, the distinction is scientifically meaningless. This is positivism at its worst: an outright conflation of epistemology with ontology. Epistemic or experimental indistinguishability is not the same thing as ontological equivalence. Even if, contrary to the pull of our present argumentation, we could not theoretically or observationally settle the question of whether our universe has a finite or infinite past, the question is still a genuine one and, metaphysically speaking, it has a correct answer. Philosophical overtures in the direction of ontological deflation are non sequiturs, pure and simple. And what is more, though we cannot explore the necessity and significance of the principle of sufficient reason here, even if the universe had an infinite past, the contingency of its existence and properties would demand an explanation that transcends the resources of philosophical naturalism. But this is a topic for another time. For now, it suffices to note that a cyclic cosmology without a beginning cannot be saved by confusing epistemology with ontology.
Where Things Stand So Far
Bouncing and, more broadly, cyclic cosmologies are bracketed by various theorems. The BGV theorem provides a kinematic constraint. Any universe with a positive average expansion rate along past-directed worldlines is past-incomplete. But then the Tolman entropy problem prevents an infinite history of BGV-avoiding bounces because accumulating entropy leads to heat death. If the scale factor grows fast enough to dilute entropy by continually increasing the volume, however, then the Kinney-Stein result guarantees it no longer avoids the BGV theorem. Wall’s quantum singularity theorem further constrains these cyclic models thermodynamically, closing the loopholes in the classical singularity theorems that quantum negative energies could otherwise exploit. In light of the seeming intractability of past-eternal bouncing cosmologies under the constraints of these various theorems, then, alternative cosmologies trying to rescue an eternal past have been pursued, and six of these “rescue” strategies have been seen to fail.
If we postulate an asymptotic past of some kind from which the universe supposedly emerged, we find that the four approaches pursuing this evasion tactic fail in different, but often similar, ways. All four are vulnerable to a general quantum-theoretic principle that may receive different expression in light of the specific features of the model. The principle in question is that whatever initial structure is able to produce an evolving cosmos must contain the seeds of this evolution, and quantum-theoretically, an effective seed must have a non-zero probability to activate that development. If the past were infinite, it would have activated an infinitely long time ago, so the past cannot be infinite and the model requires an effective beginning. The manifestation of this principle varies among the four approaches because the structural foundations of the models differ. The first model, the Ellis-Maartens emergent universe proposal, falls to the precise quantum-mechanical instability that is the focus of the Mithani-Vilenkin tunneling argument. The Aguirre-Gratton two-branch de Sitter model is derailed by the boundary surface functioning as an effective beginning and the usual pathologies of eternal inflation, as well as by the quantum disruption of its fine-tuned boundary over an infinite past. Ijjas-Steinhardt slow contraction from a Minkowski-like spacetime, requires the initial state to be unnaturally fine-tuned to an extremely low entropy and the ekpyrotic field that drives its contraction is quantum-mechanically unstable over infinite past time, precluding its past-eternality. Finally, Carroll-Chen spontaneous inflation fails because its near-Minkowski substrate is crushed by Vilenkin’s dilemma. On the one hand, if the substrate is non-singular, its Cauchy surface is rendered compact (finite) and the overall structure becomes akin to a two-branch Aguirre-Gratton construction with all its attendant problems. On the other hand, if singularities are permitted, its inflating regions are bounded by these singularities. It’s a dead-end for past-eternality either way. Beyond this, the postulated “natural” ground state is finely tuned, and the quantum fluctuations on which it relies for generating universes lead to the measure problem and Boltzmann brain dominance, epistemically undermining the model. The final model, In addition, any cyclic extension of the model is barred from infinitely many cycles by the familiar thermodynamic dilemma—either entropy accumulates across cycles and the absence of heat death rules out an infinite past sequence of them, or an expanding scale factor that dilutes entropy makes it subject to the BGV theorem via the Kinney-Stein result.
As for the remaining two cases, selectively changing the conformal frame does not objectively remove the universe’s beginning; it defines it out of existence by moving to a descriptive frame in which it is invisible. Finally, the attempt to deflate the question of a beginning by appeal to observational indistinguishability conflates ontology with epistemology. It mistakes a limit on observation for the absence of a fact of the matter. What is more, the claimed indistinguishability and equal tenability are contrary to what we have seen. None of these strategies works, so the bouncing and cyclic cosmologies examined so far do not deliver on the goal of offering a beginningless universe.
But our discussion is not done. There are two proposals in the quest for endless cycling that remain to be considered. They are sufficiently unlike the models treated here as to earn their own separate treatment. Loop quantum cosmology avoids a singular big bang with a bounce that is required by its treatment of space itself as discrete at the smallest scale. The question of the nature of this bounce and whether it can be repeated in an endless cycle from past eternity is the focus of the second installment. The last model, Penrose’s conformal cyclic cosmology (CCC), which we will consider in two final installments, is the most peculiar yet. It paradoxically lays claim to cycles without a bounce of any kind. As we will see, neither of these final two efforts rescues a beginningless universe; in fact, a primary reason for the failure of CCC rests on its use of the same strategy that undid the BST bounce, namely, the retreat into a conformal description that is blind to the beginning it is meant to eliminate.
Editor’s note: This article was updated on June 10, 2026.
Notes
- Geodesics are paths through spacetime that objects follow when the only thing acting on them is gravity. This trajectory is a straight line in flat space, but in the curved spacetime of general relativity, it is the straightest path the geometry allows. For the purposes of the BGV theorem, the relevant geodesics are the worldlines that are natural in physics—the paths of freely falling observers (timelike geodesics) and the paths of light rays (null geodesics). Such paths are complete if they can be extended indefinitely and incomplete if they cannot. Saying that the universe is “geodesically past-incomplete” is saying that every such path traced backward has finite extent—that a clock carried by a freely falling observer would record only a finite past and a light ray, which carries no clock, would end after a finite range. Under the condition of positive average expansion required by the BGV theorem, the expanding universe has an edge in the past rather than an infinite history. This edge doesn’t have to be a singularity; it is just the broader conclusion that such a universe has a beginning.
- “Semi-classical” approaches treat spacetime itself as a smooth, continuous manifold, while quantizing the matter and fields within it. Wall’s proof of the GSL and his quantum singularity theorem are semi-classical in this sense because they rely on a continuous classical manifold. The quantum cosmologies of Hartle-Hawking, Vilenkin, and Feldbrugge-Lehners-Turok retain a continuous manifold while quantizing the geometry. Loop quantum cosmology, however, is based on loop quantum gravity in which spacetime is fundamentally discrete, so no continuous manifold underlies it.
- A conformal frame is, in effect, a local ruler-and-clock convention for a spacetime. It represents a choice of how lengths and durations are to be measured. While different conformal frames disagree about those lengths and durations, possibly by a different factor from one place to another, they agree about angles and causality (which events can influence which). In ordinary physics you can’t switch between such conventions freely, because the scale of things itself is physical. By contrast, the Bars-Steinhardt-Turok framework is constructed so that no physical prediction depends on the conformal frame chosen, which is precisely what is meant by conformal symmetry.
- Changing conformal frames affects total entropy and entropy density very differently. Total entropy is just a plain count of microscopic states in a region. Changing frames cannot alter it, and it increases every cycle. Entropy density, on the other hand, is that total divided by a volume that is rescaled by a change of conformal frame. Since a frame can be chosen whose volume grows from cycle to cycle as fast as the entropy, the ratio that constitutes the density holds steady. Nothing has actually been diluted, however. The total still climbs and the universe drifts into heat death just the same, while the density has been kept level on paper. There remains just one way to hold the density constant in actuality, namely, for the universe genuinely to expand from cycle to cycle, thus spreading each cycle’s entropy through real additional volume. But real expansion across cycles is precisely the positive average expansion that the BGV theorem needs. A level entropy density thus signals either a beginning via the BGV theorem, or a bookkeeping trick that conceals one. Were the universe infinitely old, it would have reached heat death an infinite time ago. It has not, so it is not.