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Cycles of Time

Cycles of Time: An Extraordinary New View of the Universe is a 2010 book by British mathematical physicist Roger Penrose, in which he introduces his theory of conformal cyclic cosmology (CCC), proposing that the universe cycles through an infinite sequence of expanding "aeons," where the far future of one aeon—dominated by massless particles and increasing scale—conformally rescales to match the Big Bang conditions of the next.^[1] In this model, the end of the universe is not a heat death but a transition point where spatial geometry becomes indistinguishable from the initial inflationary phase, addressing fundamental questions in cosmology such as the origin of the universe's low-entropy state and the nature of black holes.^[2] Penrose, a Nobel laureate in Physics for his work on black hole singularities, builds on concepts from general relativity and conformal geometry to argue that the second law of thermodynamics, which drives entropy toward a maximum, does not preclude cyclic renewal because massive particles decay over immense timescales, leaving a universe of photons and gravitons whose causal structure loops eternally.^[1] The book explores how CCC resolves the black hole information paradox by suggesting that information from previous aeons could imprint on the cosmic microwave background (CMB) as detectable Hawking points—circular spots of anomalous temperature in the sky.^[3] It also posits that cosmic structure, including galaxy distributions, arises from irregularities in prior aeons, providing a mechanism for order without invoking multiverses or fine-tuning.^[2] Published by The Bodley Head in the UK and Knopf in the US, Cycles of Time extends Penrose's earlier ideas from works like The Road to Reality (2004), blending rigorous mathematics with accessible explanations for a general audience while challenging the standard Lambda-CDM model of cosmology.^[1] The theory has sparked debate, with proponents citing potential CMB evidence from Planck satellite data and critics questioning the assumptions about massless particle dominance and conformal rescaling's physical validity.^[4] Overall, the book offers a provocative vision of an eternal, self-renewing cosmos that reimagines time's arrow and humanity's place within it.^[5]

Background

Author and Context

Roger Penrose, a British mathematical physicist born in 1931, has made seminal contributions to cosmology and general relativity throughout his career. In the 1960s, he developed the singularity theorems, which demonstrate that singularities—points of infinite density—are inevitable outcomes in gravitational collapse under general relativity, providing a theoretical foundation for black hole formation without relying on special symmetries.^[6] These theorems, later extended in collaboration with Stephen Hawking, established that the Big Bang itself originates from such a singularity.^[7] Penrose also pioneered twistor theory in 1967, a geometric framework aimed at unifying quantum mechanics and general relativity by reformulating space-time in terms of complex variables called twistors, influencing subsequent research in quantum gravity and particle physics.^[8] His work culminated in the 2020 Nobel Prize in Physics, awarded for proving that black hole formation is a robust prediction of general relativity, shared with Reinhard Genzel and Andrea Ghez for observational confirmations.^[9] Penrose's longstanding interest in quantum gravity and cosmology is evident in his earlier popular science books, which laid intellectual groundwork for his later cosmological proposals. In The Emperor's New Mind (1989), he explores the limitations of computational models of the mind, arguing that human consciousness involves non-algorithmic processes tied to quantum mechanics and gravity, while discussing black holes, thermodynamics, and the universe's large-scale structure as key to understanding physical laws beyond classical computation.^[10] This work highlights his skepticism toward purely mechanistic views of physics, foreshadowing his critiques of standard cosmological models. Similarly, The Road to Reality (2004), a comprehensive survey of modern physics, delves into the mathematical underpinnings of relativity, quantum field theory, and cosmology, emphasizing unresolved tensions between quantum mechanics and gravity, as well as the universe's foundational structures like black holes and the Big Bang.^[11] These texts reflect Penrose's broader quest to reconcile fundamental physical theories, influencing his development of alternative cosmological ideas. The intellectual context for Cycles of Time emerged from post-2000s debates in cosmology, where the standard Big Bang model with cosmic inflation faced challenges regarding the universe's initial low-entropy state, the nature of dark energy accelerating expansion, and the irreversible arrow of time.^[12] Inflation, while successful in explaining cosmic homogeneity, struggled to address fine-tuning issues and the origin of its own parameters, prompting alternatives to avoid an unobservable pre-inflationary era.^[12] Dark energy, inferred from late-1990s supernova observations, raised questions about the universe's ultimate fate and thermodynamic consistency, while the arrow of time highlighted puzzles about why entropy increases forward but not backward from the Big Bang.^[12] Penrose's conformal cyclic cosmology, proposed in the book, offers a solution by envisioning successive universes linked conformally, addressing these issues without invoking inflation or singular beginnings.^[13]

Publication Details

Cycles of Time was first published in hardcover by The Bodley Head in the United Kingdom on 11 October 2010 and by Alfred A. Knopf in the United States on 3 May 2011.^[14] The release occurred amid growing interest in alternative cosmologies, spurred by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite's data releases from 2003 to 2010, which provided high-resolution maps of the cosmic microwave background and prompted reevaluations of standard Big Bang models, including entropy issues at the universe's origin. A paperback edition followed in the UK from Vintage on 3 October 2011, while the US paperback appeared from Vintage Books on 1 May 2012.^[15]^[1] The book has been translated into several languages, including German (Zyklen der Zeit, published by Springer in 2011), French (Les Cycles du temps, by Odile Jacob in 2013), and Spanish (Ciclos del tiempo, by Debolsillo in 2011).^[16] To promote the book, Penrose delivered related public lectures around its 2010 release, such as the Copernicus Center lecture "Aeons before the Big Bang" in Kraków, Poland, where he discussed preconformal aeons and cyclic universe concepts central to the work.^[17]

Overview

Synopsis

In Cycles of Time, Roger Penrose presents a radical reinterpretation of the universe's history and future, arguing that it undergoes an infinite sequence of cycles known as aeons, where the distant future of one aeon conformally rescales to become the Big Bang of the next. This conformal cyclic cosmology (CCC) posits that the universe's expansion leads to a state dominated by massless particles, effectively erasing scales and allowing the end of one cycle to seamlessly transition into the origin of another without invoking singularities or a true beginning. Penrose emphasizes that this model resolves longstanding puzzles in cosmology by linking the smooth, low-entropy state of the Big Bang to the similarly uniform, high-entropy future, where gravitational records of structure are lost.^[5]^[18] Penrose begins by critiquing the standard Big Bang model, highlighting its failure to explain the extraordinarily low entropy at the universe's outset, which contradicts the second law of thermodynamics that entropy must increase over time. He argues that conventional cosmology, reliant on inflation or multiverse theories, introduces unnecessary complexities and philosophical issues, such as an unexplained initial state. Instead, CCC offers a elegant alternative: as the universe ages, black holes evaporate via Hawking radiation, and matter decays into photons and other massless entities, causing the cosmos to "forget" its past through the dilution of information and the dominance of entropy. This forgetting mechanism ensures that each new aeon starts afresh, with no memory of prior cycles, yet potentially retaining subtle imprints observable in cosmic microwave background radiation.^[19] The book's narrative progresses from these thermodynamic challenges to a detailed exposition of CCC, drawing on Penrose's expertise in general relativity and conformal geometry to propose testable predictions, such as circular patterns in the cosmic microwave background from previous aeons' black hole events. By avoiding ad hoc additions like dark energy fine-tuning, Penrose envisions an eternal universe that cycles indefinitely, challenging the notion of a heat death and suggesting a more dynamic cosmic evolution.^[5]^[18]

Book Structure

The book Cycles of Time is structured around three main parts that progressively address thermodynamic and cosmological challenges before proposing Penrose's alternative model. Part I, "The Second Law and its underlying mystery," examines foundational puzzles in thermodynamics and their implications for the universe's origins, beginning with Chapter 1, which explores the remarkably low entropy state at the Big Bang.^[20] Part II, "The oddly special nature of the Big Bang," delves into cosmological anomalies, such as the uniformity and flatness of the early universe, highlighting tensions with standard inflationary models.^[20] Part III, "Conformal cyclic cosmology," introduces the geometric framework for cyclic universes and discusses potential evidence, including observational tests like patterns in the cosmic microwave background.^[20] Spanning 27 chapters in total, the volume transitions smoothly from problem identification in the early parts to solution and verification in the later ones, supported by appendices that provide essential mathematical derivations for advanced readers.^[1] Penrose employs a distinctive writing approach, featuring hand-drawn diagrams to visualize abstract concepts like conformal rescaling and spacetime geometry, while balancing accessible prose for general audiences with rigorous technical digressions for specialists.^[21] This structure ensures conceptual progression without overwhelming detail, allowing readers to grasp the cyclic model's novelty as an elegant resolution to entropy and origin paradoxes.

Scientific Foundations

Thermodynamic Challenges

The second law of thermodynamics states that the entropy of an isolated system cannot decrease over time; instead, it remains constant for reversible processes or increases for irreversible ones, as mathematically expressed by the inequality S_{\text{final}} > S_{\text{initial}}. This principle, first articulated by Rudolf Clausius in 1850, dictates that natural processes tend toward greater disorder, providing a fundamental asymmetry in physical laws. In the context of cosmology, the universe is regarded as an isolated system, implying that its total entropy has been monotonically increasing since the Big Bang. A profound challenge arises from the extraordinarily low entropy of the early universe at the Big Bang, which contradicts expectations under standard thermodynamic evolution. Roger Penrose has calculated that the probability of the universe assuming such a highly ordered, low-entropy initial state—smooth and uniform on vast scales—is vanishingly small, approximately 1 in $10^{10^{123}}, a number derived from the phase-space volume of possible initial configurations compared to the actual one observed. This estimate underscores the improbability: among all conceivable initial states consistent with general relativity, the low-entropy Big Bang occupies an infinitesimally tiny fraction of the available possibilities. Standard inflationary models, while addressing spatial uniformity, fail to explain this thermodynamic anomaly, as they require even lower initial entropy to initiate expansion, exacerbating the puzzle rather than resolving it. The low-entropy origin of the universe directly underpins the arrow of time, the irreversible progression from past to future that governs everyday phenomena like the spreading of heat or the decay of structures. This temporal directionality emerges from the entropy gradient established at the Big Bang, where the universe's initial smoothness created a vast potential for entropy increase, driving all subsequent irreversible processes forward in time. Penrose emphasizes that without this primordial low-entropy condition, the second law would lack a clear starting point, rendering the observed asymmetry of time inexplicable within conventional cosmology. In "Cycles of Time," he critiques how this unexplained feature highlights a foundational gap in understanding the universe's thermodynamic history.

Cosmological Puzzles

The horizon problem arises in standard Big Bang cosmology because the cosmic microwave background (CMB) exhibits remarkable uniformity in temperature across the sky, with variations of only about 1 part in 100,000, despite the fact that opposite regions of the observable universe were never in causal contact during the early hot phase when the CMB was emitted.^[22] In the conventional model, light from these distant regions could not have traveled far enough to equalize temperatures, as the particle horizon at recombination limits causal connections to scales much smaller than the current observable universe. Roger Penrose highlights this as a profound puzzle, emphasizing that the observed large-scale homogeneity demands an explanation beyond standard causality in the Big Bang framework.^[23] The flatness problem refers to the universe's density parameter Ω, which observations indicate is extremely close to 1 (Ω ≈ 1.00 ± 0.02 from CMB data), implying a nearly flat spatial geometry that requires exquisite fine-tuning in the early universe.^[24] Without such tuning, the evolution of the Friedmann equation would cause Ω to deviate rapidly from 1 over cosmic time: for a matter-dominated universe, |1 - Ω| grows proportional to the scale factor, making the current near-critical density unstable unless initial conditions were precisely adjusted to within 10^{-60} or better at the Planck epoch.^[25] Penrose underscores this as evidence of unnatural initial conditions in Big Bang models, where the required precision appears improbably specific without additional mechanisms.^[23] Penrose critiques the inflationary paradigm, proposed to resolve these issues through rapid exponential expansion, as ultimately inadequate because it merely shifts the fine-tuning to the inflaton field's initial conditions and fails to address the low-entropy state of the universe.^[23] While inflation can smooth out initial irregularities to explain horizon and flatness puzzles, it introduces new challenges, such as the measure problem in eternal inflation scenarios, where defining probabilities across an infinite multiverse of bubble universes lacks a natural, observer-independent measure, leading to ambiguous predictions for cosmic observables.^[26] These spatial and density uniformity issues are compounded by the temporal puzzle of low initial entropy, further straining inflationary explanations.^[23]

Conformal Cyclic Cosmology

Conformal Geometry Basics

Conformal geometry provides essential mathematical tools for analyzing the structure of spacetime in general relativity, particularly at its boundaries and singularities, by preserving angles while allowing for rescaling of distances. A conformal transformation is an angle-preserving map between Riemannian manifolds that rescales the metric tensor by a positive smooth function \Omega, such that the transformed metric satisfies \hat{g}_{ab} = \Omega^2 g_{ab}, where g_{ab} is the original metric.^[27] This rescaling, often denoted as ds'^2 = \Omega^2 ds^2, enables the extension of physical spacetimes to include infinite regions without altering the causal structure or light cone angles.^[28] Such transformations are crucial in general relativity because they allow physicists to compactify unbounded spacetimes into finite manifolds, facilitating the study of asymptotic behaviors.^[27] One key application of conformal geometry is the concept of conformal infinity, which describes the boundary of spacetime in asymptotically flat or de Sitter-like universes. Introduced by Roger Penrose, this involves conformally compactifying the physical spacetime manifold M with metric g to a larger unphysical manifold \bar{M} with metric \hat{g} = \Omega^2 g, where \Omega \to 0 at the boundary \partial M.^[28] The resulting structure, visualized in Penrose diagrams, represents null infinity (\mathcal{I}^\pm), spacelike infinity (i^0), and timelike infinities (i^\pm) as points or curves on a compact diagram, preserving the conformal class of the metric.^[27] These diagrams, which transform infinite distances into finite ones via the conformal factor, reveal the global causal relations and peeling properties of gravitational fields near infinity.^[28] The Weyl tensor C_{abcd} plays a central role in conformal geometry as the conformally invariant part of the Riemann curvature tensor, measuring gravitational tidal distortions independent of local mass-energy content captured by the Ricci tensor.^[27] Unlike the full Riemann tensor, the Weyl tensor remains unchanged under conformal rescalings, making it a key quantity for analyzing spacetime geometry across different scales.^[29] Penrose's Weyl curvature hypothesis posits that at the initial singularity of the universe, such as the Big Bang, the Weyl tensor approaches zero (C_{abcd} \to 0), reflecting a highly symmetric, low-entropy state with minimal tidal distortions.^[29] This vanishing ensures compatibility with conformal compactification at the boundary between cosmological aeons, where smooth transitions require negligible Weyl curvature.^[29]

The Cyclic Universe Model

In Roger Penrose's Conformal Cyclic Cosmology (CCC), the universe consists of an infinite sequence of aeons, where each aeon represents a complete cosmological history beginning with a Big Bang and evolving through expansion dominated initially by massive particles, then transitioning to a phase where massive matter decays and only massless particles, such as photons and gravitons, remain dominant.^[30] As the aeon progresses toward its remote future, the universe undergoes infinite expansion driven by a positive cosmological constant, leading to an exponentially dilute state where spatial scales become irrelevant due to the absence of massive objects.^[30] This far-future configuration, characterized by a smooth, homogeneous distribution of massless radiation, is then conformally rescaled—using the transformation \hat{g}_{ab} = \Omega^2 g_{ab} where \Omega approaches zero—to match the geometry of a low-entropy Big Bang for the subsequent aeon, effectively linking the infinite future of one cycle to the origin of the next without invoking a singularity.^[30] The model's resolution of the thermodynamic arrow of time hinges on an entropy reset mechanism at the transition between aeons. In the distant future of each aeon, all black holes, which would otherwise retain high gravitational entropy through their event horizons, completely evaporate via Hawking radiation over immense timescales, dispersing their mass-energy into massless particles and leaving no persistent records of prior gravitational structures.^[30] With the disappearance of massive particles and scales, the universe achieves a state of conformal invariance, where physical distinctions dependent on size or mass are erased, allowing the Weyl curvature tensor—responsible for gravitational irregularities—to approach zero, thereby establishing a smooth, low-entropy initial condition for the next aeon as per the Weyl Curvature Hypothesis.^[30] This process ensures that entropy effectively restarts at a low value, addressing the puzzle of why our universe began in such an ordered state without requiring special initial conditions. CCC posits an eternal succession of aeons extending infinitely into both the past and future, circumventing the implications of classical singularity theorems by conformally joining the boundaries between cycles rather than positing a unique origin or endpoint.^[30] In this framework, there is no absolute beginning to the cosmos, as each Big Bang emerges from the rescaled remnants of a prior aeon, providing a deterministic yet cyclic evolution that aligns with general relativity's conformal structure.^[30]

Evidence and Implications

Proposed Evidence

Penrose interprets certain anomalies in the cosmic microwave background (CMB) as supporting evidence for conformal cyclic cosmology (CCC), particularly through the identification of "Hawking points"—anomalous circular hot spots of raised temperature, interpreted as imprints of Hawking radiation from supermassive black hole evaporations in a preceding aeon, often surrounded by low-variance concentric circles. These features manifest as nearly circular spots with angular diameters of approximately 3–4 degrees, where the radiation from evaporated black holes (with masses up to $10^{14} solar masses) becomes conformally mapped onto the CMB sky of the subsequent aeon. An initial analysis in 2010 using Wilkinson Microwave Anisotropy Probe (WMAP) data identified concentric low-variance circles consistent with this prediction, with a non-isotropic distribution suggesting alignment with specific past aeon events. A 2013 follow-up study reinforced these findings in WMAP data, detecting multiple sets of such circles with statistical significance exceeding random expectation.^[31] Subsequent examination of Planck satellite data from the 2013 release, culminating in a 2020 analysis, claimed the presence of over 20 such anomalous hot spots with greater than 99.98% confidence compared to simulated CMB maps, though subsequent re-evaluations reduced this to approximately 87% confidence, with positions aligning across independent datasets despite differing instrumental noise.^[32] However, these findings remain controversial, with critics arguing the anomalies are consistent with statistical fluctuations or instrumental effects in standard inflationary models, and no broad acceptance as of 2025.^[33]^[34] A core aspect of CCC's evidential framework is its explanation for the observed low entropy and uniformity of the CMB without invoking cosmic inflation. In this model, the distant future of one aeon—characterized by a smooth, radiation-dominated, asymptotically flat spacetime with vanishingly small residual entropy after black hole evaporation—conformally rescales to match the high-entropy boundary conditions of the next aeon's Big Bang, thereby "inheriting" a low-entropy initial state dominated by gravitational degrees of freedom. This conformal smoothness ensures the CMB's near-perfect isotropy, as irregularities from the previous aeon are diluted in the infinite expansion, providing a thermodynamic bridge across cycles. Penrose argues this resolves the fine-tuning problem of the universe's initial conditions, where the second law of thermodynamics emerges from gravitational clumping rather than an ad hoc low-entropy assumption. Penrose also cites potential links between the large-scale distribution of galaxies in our aeon and residual structures from the prior aeon, detectable through cross-correlations in surveys of cosmic structure. In CCC, supermassive black hole mergers or collisions in galaxy clusters of the previous aeon would emit gravitational waves that propagate across the conformal boundary, imprinting subtle angular correlations or alignments in the present universe's matter distribution. Early explorations using data from large-scale structure surveys, such as those mapping galaxy clusters, have sought these signatures, though results remain tentative and consistent with expected clustering from standard cosmology. Such correlations, if confirmed, would indicate inheritance of non-trivial topology from past cycles, beyond random fluctuations.

Testable Predictions

Conformal Cyclic Cosmology (CCC) proposes several falsifiable predictions that distinguish it from standard inflationary models, primarily through observable imprints from previous aeons preserved across conformal boundaries. One key prediction involves concentric circles of unusually low variance in the cosmic microwave background (CMB), arising from gravitational wave bursts produced by supermassive black hole mergers in a prior aeon. These bursts create nearly isotropic spherical wavefronts that intersect the CMB last-scattering surface, manifesting as circular rings with low temperature fluctuations due to non-additive averaging effects at overlapping regions. The predicted angular radii of these rings range from approximately 2.5° to 16°, corresponding to the angular diameter distance in the previous aeon, with no rings expected beyond about 20°; analysis of Wilkinson Microwave Anisotropy Probe (WMAP) data has been suggested as a means to detect such patterns, where multiple concentric sets (e.g., families of three or more rings) would indicate clustered black hole encounters in galactic superclusters.^[31] Another testable aspect concerns gravitational wave signals from prior aeons, which could imprint on the CMB as B-mode polarization patterns or tensor perturbations. In CCC, the evaporation of supermassive black holes—termed "Hawking points"—at the end of a previous aeon releases energetic photons and gravitational waves that propagate conformally into our aeon, potentially correlating with hot spots in the CMB surrounded by concentric low-variance rings. These signals may appear as localized B-mode anomalies, such as those tentatively identified near the BICEP2 detection region, offering a way to probe pre-Big Bang tensor modes without relying on primordial gravitational waves from inflation. Additionally, CCC proposes that erebons—hypothetical dark matter particles of ~10^{-5} g—could produce high-frequency impulsive gravitational waves detectable as correlated low-level noise in interferometers like LIGO, with specific time delays (e.g., 6.9 ms between Hanford and Livingston sites) tied to galactic sources, though no such detections have been reported as of 2025. Philosophically, CCC implies no requirement for fine-tuning of initial conditions, as the infinite sequence of aeons allows rare, low-entropy configurations—like our observed universe—to emerge naturally without invoking a multiverse. Each cycle resets the conformal structure while preserving causal influences from black hole remnants, enabling an eternal cosmos that circumvents the singularities and entropy issues of standard Big Bang models. This framework predicts ongoing cycles without beginning or end, potentially resolvable through future high-resolution CMB polarization surveys or advanced gravitational wave detectors.

Reception

Academic Reviews

Lee Smolin praised Roger Penrose's Cycles of Time for its innovative approach to cosmology, particularly for proposing a model that circumvents the fine-tuning problems associated with cosmic inflation by relying on conformal rescaling across aeons.^[35] Smolin highlighted the book's masterful pedagogy in explaining complex thermodynamic concepts, noting how the conformal cyclic cosmology (CCC) framework addresses the low-entropy initial state of the universe without invoking inflationary mechanisms that require precise parameter adjustments.^[35] Criticisms, however, center on the unproven nature of Penrose's Weyl curvature hypothesis, which posits that the Weyl tensor vanishes at the Big Bang to ensure low gravitational entropy. This remains a classical conjecture without robust quantum validation, particularly in contexts like loop quantum cosmology. Additionally, the model's lack of integration with quantum gravity theories has been noted as a limitation, as CCC operates primarily within general relativity without addressing quantum effects at singularities. These discussions underscore the speculative elements of the model while acknowledging its provocative challenge to standard cosmology.

Popular and Scientific Impact

The publication of Cycles of Time garnered significant media coverage, with a prominent review in The Guardian in 2010 highlighting the book's cyclic cosmology as an appealing solution to longstanding questions about the universe's origins and fate.^[5] Post-publication, Penrose extended the discussion through public lectures, including a 2011 TEDx talk at the University of Warwick on space-time geometry and novel cosmological models, which drew from the conformal cyclic framework outlined in the book.^[36] The book's ideas have left a lasting scientific legacy by spurring research in conformal cyclic cosmology (CCC). A key example is Penrose's 2018 collaboration with Daniel An, Krzysztof A. Meissner, and Paweł Nurowski, which analyzed cosmic microwave background (CMB) data to identify anomalous hot spots interpreted as Hawking points—potential remnants of evaporating supermassive black holes from a prior aeon.^[4] This work, published in Monthly Notices of the Royal Astronomical Society in 2020, built directly on the theoretical foundations of Cycles of Time.^[32] Furthermore, CCC has influenced broader debates in cosmology by proposing a viable alternative to the standard ΛCDM model, eschewing cosmic inflation in favor of successive conformal aeons that address issues like the low-entropy initial state of the universe.^[37]^[38] Research on CCC continues as of 2025, with recent publications exploring its physical implications and addressing criticisms regarding conformal rescaling and evidence from CMB data.^[3] Beyond academia, Cycles of Time has contributed to popularizing advanced concepts such as conformal rescaling and eternal cosmic cycles, fostering public interest in non-standard cosmologies through its accessible yet rigorous exposition. Academic critiques of the model, while noting evidential challenges, have underscored its role in stimulating interdisciplinary discussions on the universe's structure.^[13]

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