Big Bounce

Run the history of the universe backwards and everything gets closer together. Galaxies that are now receding from one another converge. The cosmic microwave background, today a faint glow at about 2.7 degrees above absolute zero, heats up into a blinding plasma. Eventually density and temperature climb without limit. In the equations of general relativity, the film ends at a single instant where the numbers become infinite: the initial singularity, usually called the Big Bang.

That endpoint has always been uncomfortable. An infinite density is not a physical state. It is a sign that the theory has been pushed beyond the range where it can be trusted. So a natural question follows: if the equations fail there, what really happened?

One family of answers says the film does not end at all. Before the Big Bang there was a contracting universe, which shrank to an extremely dense but finite state and then rebounded into the expansion we observe. If that happened once, it might have happened many times. This is the idea of the Big Bounce, and of the cyclic universe built from repeated bounces.

The idea is old, mathematically serious, and currently unconfirmed. Its modern versions differ sharply from the popular image of identical universes repeating forever, and some make claims that observations could test.

A Bounce Is Not Necessarily a Cycle

Throw a ball upward. It slows, stops, and falls. Now imagine that when it hits the ground, instead of stopping, it bounces back up, and then falls again. A bouncing universe applies the same picture to cosmic size: expansion slows, turns into contraction, contraction reaches a minimum size, and the universe rebounds.

Two separate claims hide inside this picture, and they should be kept apart:

1. A bounce: our expanding phase was preceded by a contracting phase, joined by a finite "bounce" rather than an infinite singularity.
2. Cycles: this sequence of expansion, contraction and bounce repeats, possibly forever into the past and future.

A model can have one bounce without endless cycles. And a model can be cyclic without the cycles being copies of one another. These distinctions matter more than any other point in the subject.

The Formal Description: Why a Bounce Is Hard

The Friedmann Equations

Modern cosmology describes the average behaviour of the universe with a single function of time, the scale factor $a(t)$, which measures how far apart typical galaxies are. Its growth rate is the Hubble parameter $H = \dot a / a$, where the dot means a time derivative. General relativity, applied to a uniform universe, gives the Friedmann equations:

where:

• $G$ is Newton's gravitational constant and $c$ the speed of light;
• $\rho$ is the density of matter and radiation, and $p$ its pressure;
• $k$ describes spatial curvature: $+1$ for a closed universe (finite, like the surface of a sphere), $0$ for flat, $-1$ for open;
• $\Lambda$ is the cosmological constant, the simplest form of dark energy.

The first equation is an energy balance: gravity's pull (the density term) against the motion of expansion. The second says ordinary matter and radiation always decelerate the expansion.

Friedmann's "Periodic World"

In 1922 Alexander Friedmann found that for a closed universe, the scale factor can rise from zero, reach a maximum, and fall back to zero. He explicitly named this case the "periodic world" ^[1,3]. In a popular book published in 1923, he remarked that this brought to mind the cycles of existence described in Hindu cosmology, while cautioning that such ideas were at present only curiosities ^[3]. In 1924 he extended the analysis to open universes with negative curvature, which expand forever ^[2].

This is the origin of the oscillating universe in modern physics. But notice what the mathematics actually gives: each "cycle" begins and ends at $a = 0$, a singularity where density is infinite. The equations do not say how one cycle connects to the next. The bounce is assumed, not derived.

The Singularity Theorems

In the 1960s, Roger Penrose and Stephen Hawking proved that this problem is not an artefact of assuming perfect uniformity. Under broad conditions, including that matter has positive energy and gravity is always attractive, general relativity requires a singularity in the past of an expanding universe like ours ^[4].

A bounce therefore needs one of two things:

• New physics that makes gravity effectively repulsive at very high density. For a flat universe, the Friedmann equations give $\dot H = -4\pi G(\rho + p/c^2)$. At a bounce, $H$ passes from negative to positive, so $\dot H > 0$, which requires $\rho + p/c^2 < 0$. Ordinary matter never does this. Physicists call this a violation of the null energy condition.
• A quantum theory of gravity that replaces general relativity at the Planck scale, where quantum effects on spacetime itself become important.

Every bounce model is, at bottom, a proposal for one of these.

Historical Development

Tolman and the Entropy Problem

In the early 1930s, Richard Tolman at Caltech made the first careful study of oscillating universes including thermodynamics ^[5,6]. The key question was the second law of thermodynamics: in any closed system, entropy, roughly a measure of disorder, never decreases.

If a universe cycles, entropy produced in one cycle (starlight, heat, black holes) should carry over to the next. In his 1931 papers Tolman argued that relativistic thermodynamics does not forbid repeated expansion and contraction ^[5,6]. His further analysis, completed in the following years and in his 1934 textbook, showed that entropy increase changes the cycles: extra entropy means extra radiation pressure, which makes each successive cycle expand to a larger maximum size and last longer than the one before ^[3]. As the historian Helge Kragh summarises, the simple picture of identical cycles had to be replaced by one of cycles growing ever larger ^[3].

This creates two problems:

1. The cycles are not repetitions. They form a sequence with a direction.
2. The past may not be infinite. Run the sequence backwards and cycles get smaller and shorter. It is not obvious that the chain can extend infinitely into the past rather than starting somewhere.

This is known as Tolman's entropy problem, and every later cyclic model has had to answer it.

The Oscillating Model Falls Out of Favour

Through much of the twentieth century, the oscillating universe stayed on the edge of cosmology. The singularity theorems made the bounce itself look impossible in classical physics. And from 1998, supernova observations showed that the expansion of the universe is accelerating, driven by what is now called dark energy ^[7,8]. If dark energy is a true cosmological constant, the universe will expand forever and never recollapse. The simple Friedmann oscillation, with gravity eventually pulling everything back together, does not describe the universe we observe.

Bounce ideas returned in the 2000s in new forms, each tied to a specific proposal for new physics.

Modern Models

Loop Quantum Cosmology: A Quantum Bounce

Loop quantum gravity is an attempt to quantise spacetime itself. In it, geometry is not smooth at the smallest scales but built from discrete quanta of area and volume. Loop quantum cosmology (LQC) applies these techniques to simplified, uniform model universes.

In 2001, Martin Bojowald showed that in LQC the singularity is naturally removed: quantities that blow up classically remain finite, and the evolution can be continued through the point where the classical volume would reach zero ^[9]. In 2006, Abhay Ashtekar, Tomasz Pawłowski and Parampreet Singh constructed the quantum dynamics in detail and showed numerically that the Big Bang is replaced by a quantum bounce, with a contracting classical universe on the other side ^[10,11].

The result can be summarised by an effective, quantum-corrected Friedmann equation for a flat universe:

Here $\rho_c$ is a critical density, about 0.41 times the Planck density ^[12], the scale at which quantum gravity dominates. When $\rho \ll \rho_c$, the correction is negligible and ordinary general relativity is recovered. As $\rho$ approaches $\rho_c$, the bracket goes to zero, so $H = 0$: expansion stops and reverses. Gravity effectively becomes repulsive at Planck density.

Status: mathematical result within a candidate theory. The bounce is robust in these models. But LQC works with symmetry-reduced universes, and its derivation from full loop quantum gravity is not complete. Loop quantum gravity itself has no experimental confirmation.

The Ekpyrotic and Cyclic Models: Colliding Branes

In 2001, Justin Khoury, Burt Ovrut, Paul Steinhardt and Neil Turok proposed the ekpyrotic universe, borrowing a Stoic word for a world-ending conflagration ^[13]. The model draws on string theory and M-theory, in which our observable universe may be a three-dimensional membrane, or brane, embedded in a space with an extra dimension (compare Kaluza–Klein Reduction and 13-Dimensional Models). In this picture, the hot Big Bang corresponds to a collision between branes.

The following year Steinhardt and Turok extended this into a cyclic model ^[14,15]. In each cycle:

1. The universe expands, cools, forms galaxies, and enters a long period of dark-energy-driven acceleration.
2. That acceleration dilutes matter, radiation, entropy and black holes until each region is nearly empty.
3. The branes approach again. A slow contraction phase (the ekpyrotic phase) smooths and flattens the universe.
4. The branes collide, producing a new hot Big Bang.

This design is a direct response to Tolman. Total entropy still grows, but each observable region is emptied by the long acceleration before the next cycle begins. The authors describe this as restoring the same vacuum state before each crunch, so the cycling is an attractor that the system settles into ^[15].

The ekpyrotic phase also offers an alternative to cosmic inflation, the leading theory of the very early universe. Both explain why the universe is so uniform and flat, and both can generate the small density ripples that later grew into galaxies. They differ sharply in one prediction, discussed below.

Status: speculation grounded in a specific theoretical framework. The model depends on features of string theory that have not been tested, and whether the collision itself can be described without a singularity was a long-standing point of debate.

Ijjas and Steinhardt: A Classical, Non-Singular Bounce

Later work by Anna Ijjas and Paul Steinhardt developed bounces that are smooth and classical, avoiding the need for the universe to shrink to Planck density ^[16]. The bounce happens at densities where classical field theory still applies, using fields that temporarily violate the null energy condition in a controlled way.

In 2019 they proposed a new kind of cyclic universe ^[17]. In it, the Hubble parameter, density and temperature oscillate periodically, but the scale factor grows by a large factor from one cycle to the next. Each region of space is effectively reset, while the universe as a whole becomes enormously larger with every cycle. Entropy is not a problem in this picture because it is diluted, not because it is erased.

Note what this means for the question of repetition: the model is cyclic in its physical conditions, but it is explicitly not a loop that returns to the same state.

A related theoretical concern applies to all such models. The Borde–Guth–Vilenkin theorem shows that any spacetime which, on average, has been expanding throughout its history cannot be extended infinitely into the past along all paths ^[18]. A universe that grows every cycle is expanding on average. Whether cyclic models escape the need for some kind of beginning, or merely postpone it, remains debated.

Penrose's Conformal Cyclic Cosmology

Roger Penrose proposed a quite different cycle, called Conformal Cyclic Cosmology (CCC) ^[19]. It starts from a puzzle about entropy: the early universe was astonishingly smooth, which for gravity means extraordinarily low entropy. Why?

CCC's answer relies on the far future. After perhaps $10^{100}$ years, stars will have died, black holes will have evaporated by Hawking radiation, and the universe may contain almost nothing but massless radiation. Massless particles have no built-in sense of scale: they cannot "tell" whether the universe is huge or tiny. Penrose suggests that at this point the infinitely expanded, cold future of one era (an aeon) can be mathematically rescaled and identified with the hot, dense Big Bang of the next. There is no contraction at all. The "bounce" is a change of description.

CCC requires assumptions that go beyond known physics, including that all massive particles eventually lose their mass or decay. It is not derived from any accepted theory.

Evidence: What Could Test a Bounce?

The most important statement here is simple: no bounce has been observed. All current observations are consistent with a hot, dense early universe, and none requires a previous contracting phase. The question is whether any observation could distinguish a bounce from alternatives. Several possibilities have been proposed.

Primordial Gravitational Waves

Inflation, a brief period of extremely rapid expansion, generically produces a background of gravitational waves, which would leave a characteristic twisting pattern (called B-modes) in the polarisation of the cosmic microwave background. The strength of this signal is measured by the tensor-to-scalar ratio $r$.

The ekpyrotic and cyclic models predict that primordial gravitational waves at these scales should be far too weak to detect ^[13,14]. This is a genuine, sharp prediction.

Current measurements have not seen primordial B-modes. Combining Planck, WMAP and BICEP/Keck data gives an upper limit of $r < 0.036$ at 95% confidence ^[20,21]. This rules out many of the simplest inflation models, but does not rule out inflation as a whole. A future detection of primordial gravitational waves would strongly disfavour ekpyrotic and cyclic models. Continued non-detection would not by itself confirm them.

The Cosmic Microwave Background

Bounce models can leave subtler fingerprints in the CMB: particular patterns of non-Gaussianity (departures from a pure bell-curve distribution of temperature fluctuations), or modifications to fluctuations on the largest scales. Some LQC studies have explored effects of this kind. None has been observed at a level that requires a bounce.

The Circles and "Hawking Points" Controversy

CCC made more specific claims.

• In 2010 and 2013, Vahe Gurzadyan and Penrose reported sets of concentric circles of unusually low temperature variation in WMAP data, which they interpreted as imprints of gravitational waves from colliding supermassive black holes in the previous aeon ^[22,23].
• Independent teams re-analysed the data and found that such circles appear just as often in simulated skies with ordinary, random CMB fluctuations ^[24,25]. One group summarised that the claimed features simply rediscovered the fact that the CMB contains structure ^[25].
• In 2020, Daniel An, Krzysztof Meissner, Paweł Nurowski and Penrose reported warm spots in Planck and WMAP data, which they called Hawking points and interpreted as the final energy released by evaporating black holes in the previous aeon ^[26].
• A re-analysis the same year by Dylan Jow and Douglas Scott concluded that, once the analysis accounts for the freedom to choose ring sizes, the excess is significant at only about the 87% level, little more than one standard deviation, and therefore not statistically significant ^[27].

Assessment: the CCC signals are disputed and not accepted as evidence by most cosmologists. The case illustrates a recurring danger in searching the CMB for patterns: with enough freedom in what one looks for, apparent signals are easy to find.

Dark Energy

If dark energy is a constant, today's acceleration continues forever and simple recollapse is ruled out. Recent measurements by the DESI survey suggest, at modest significance, that dark energy may change over time ^[28]. If confirmed, this would reopen questions about the far future, including whether expansion could eventually slow or reverse. At present this remains an open observational question, not evidence for a bounce.

Do the Cycles Repeat Exactly?

A striking version of the cyclic idea imagines that every cycle is identical: the same galaxies, the same Earth, the same people, living the same lives again and again. This section treats that idea honestly, which means treating it as speculation, with a philosophical history that is older than the physics.

What Physics Says

Most models explicitly predict non-identical cycles.

• Tolman's cycles grow in size and duration because entropy accumulates ^[3].
• Steinhardt–Turok cycles reset average conditions, but the specific pattern of density ripples, and so every galaxy and star, is seeded afresh by quantum fluctuations in each cycle ^[15].
• Ijjas–Steinhardt cycles grow by an enormous factor every time ^[17].
• CCC aeons are linked, but each aeon's contents are different; the whole point of the proposed signals is that the previous aeon left a distinct imprint.
• In loop quantum cosmology, Bojowald argued in 2007 that some properties of the quantum state do not survive the bounce, a "cosmic forgetfulness" that would prevent perfect replicas ^[29]. Corichi and Singh later disputed how much is forgotten, arguing that a semiclassical universe on one side of the bounce implies one on the other ^[30]. Either way, neither paper suggests the universe after the bounce is a copy of the one before.

Poincaré Recurrence

There is one mathematical result that sounds as if it supports exact repetition. In 1890, Henri Poincaré proved that a mechanical system confined to a bounded region of its possible states, and obeying laws that conserve the volume of those states, will return arbitrarily close to its starting configuration if one waits long enough ^[31]. This Poincaré recurrence theorem is genuine mathematics.

Applying it to the universe runs into several obstacles:

• Return is close, not exact. The theorem guarantees near-repetition, not identical repetition.
• The times are absurd. For a macroscopic system, recurrence times are numbers so large that even writing them requires exponents of exponents. They dwarf any cycle length in cosmology.
• The universe may not satisfy the conditions. An expanding universe with gravity is not obviously a bounded system with a fixed set of available states.
• Quantum versions are speculative. Some physicists have argued that a universe dominated forever by a cosmological constant would have a finite number of quantum states and could therefore show recurrences. Dyson, Kleban and Susskind explored this possibility and treated its consequences as disturbing rather than as a prediction ^[32].

Assessment: exact repetition of cycles is not predicted by any established physical theory. It is compatible with some idealised mathematics, but it is not a consequence of any current bounce model.

Eternal Return as a Philosophical Idea

The image of identical recurrence has deep roots outside physics. Cyclical cosmologies appear in several ancient traditions, including Stoic philosophy and Hindu cosmology.

Its most famous modern form is Friedrich Nietzsche's eternal recurrence of the same. In The Gay Science and Thus Spoke Zarathustra, Nietzsche asked the reader to imagine that every moment of their life would return, identically, forever. Scholars debate whether he meant it as a cosmological claim, but it is most often read as an ethical test: could you affirm your life so completely that you would want it to recur infinitely? ^[33]

That question does not depend on physics. Its force comes from the thought experiment, not from any cosmological evidence. It belongs, in the terms of these articles, to symbolic or philosophical interpretation. For related questions about whether the future is fixed, see Determinism and Block Universe. For loops in time within a single universe, which are a different idea entirely, see Closed Timelike Curves and Bootstrap Paradox.

Limitations and Open Problems

• No observation requires a bounce. Standard cosmology with an early hot phase, and very likely inflation, fits the data without one.
• Every bounce needs unconfirmed physics. Quantum gravity, extra dimensions, or fields that violate standard energy conditions. None of these has independent experimental support.
• Stability is a serious concern. A contracting universe tends to become increasingly irregular, and small anisotropies can grow and destroy a smooth bounce. The ekpyrotic phase was designed to suppress this, but control of the bounce remains a technical challenge across approaches ^[34].
• The beginning may not be avoided. Entropy and theorems about expanding spacetimes suggest that even cyclic models may need some initial boundary ^[3,18].
• Information across the bounce is uncertain. What survives from one phase to the next differs between models and is not settled even within a single framework ^[29,30].
• Falsifiability varies. Ekpyrotic and cyclic models make at least one clear prediction (no detectable primordial gravitational waves at CMB scales). Other scenarios have fewer sharp predictions.

What a Bounce Would Change

The Big Bounce matters because it treats the Big Bang singularity as a question rather than an answer. General relativity says the past ends in an infinity; most physicists read that as a signal that a deeper theory is needed. Bounce models are concrete attempts to say what that theory might do.

Observation takes us back to a hot, dense universe that has expanded for about 13.8 billion years and is now expanding at an accelerating rate. It has not revealed primordial gravitational waves or any trace of a phase before that hot beginning.

Several quantum-gravity models and some classical field theories replace the singularity with a bounce; some also permit cycles. None yet tells us whether a bounce occurred, whether time had a beginning, or what could survive from one cosmic phase to the next.

The idea of an identical, endlessly repeating universe remains a powerful philosophical image. Physics, as it stands, points in a different direction: if there were earlier universes, they were most likely not copies of ours. That may be the more interesting possibility, because it suggests the history of the cosmos, like the history of life on Earth, may be a sequence that goes somewhere rather than a circle.

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