A cyclic model (or oscillating model) is any of several

cosmological model Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of f ...

s in which the

universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. A ...

follows infinite, or indefinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...

in 1930 theorized a universe following an eternal series of oscillations, each beginning with a

Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from t ...

and ending with a

Big Crunch The Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach zero, an event potent ...

; in the interim, the universe would expand for a period of time before the gravitational attraction of matter causes it to collapse back in and undergo a bounce.

Overview

In the 1920s, theoretical physicists, most notably

, considered the possibility of a cyclic model for the universe as an (everlasting) alternative to the model of an expanding universe. However, work by Richard C. Tolman in 1934 showed that these early attempts failed because of the cyclic problem: according to the

Second Law of Thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...

, entropy can only increase. This implies that successive cycles grow longer and larger. Extrapolating back in time, cycles before the present one become shorter and smaller culminating again in a Big Bang and thus not replacing it. This puzzling situation remained for many decades until the early 21st century when the recently discovered

dark energy In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the unive ...

component provided new hope for a consistent cyclic cosmology. In 2011, a five-year survey of 200,000 galaxies and spanning 7 billion years of cosmic time confirmed that "dark energy is driving our universe apart at accelerating speeds." One new cyclic model is the

brane cosmology Brane cosmology refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory. Brane and bulk The central idea is that the visible, three-dimensional universe is restricted to a brane in ...

model of the

creation of the universe The chronology of the universe describes the history and future of the universe according to Big Bang cosmology. Research published in 2015 estimates the earliest stages of the universe's existence as taking place 13.8 billion years ago, with ...

, derived from the earlier ekpyrotic model. It was proposed in 2001 by

Paul Steinhardt Paul Joseph Steinhardt (born December 25, 1952) is an American theoretical physicist whose principal research is in cosmology and condensed matter physics. He is currently the Albert Einstein Professor in Science at Princeton University, where h ...

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...

and Neil Turok of

Cambridge University , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

. The theory describes a universe exploding into existence not just once, but repeatedly over time. The theory could potentially explain why a repulsive form of energy known as the

cosmological constant In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...

, which is accelerating the expansion of the universe, is several orders of magnitude smaller than predicted by the standard

model. A different cyclic model relying on the notion of

phantom energy Phantom energy is a hypothetical form of dark energy satisfying the equation of state with w < -1. It possesses

negative k ...

was proposed in 2007 by Lauris Baum and Paul Frampton of the

University of North Carolina at Chapel Hill A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which r ...

. Other cyclic models include

conformal cyclic cosmology Conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity and proposed by theoretical physicist Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity (i.e. th ...

and

loop quantum cosmology Loop quantum cosmology (LQC) is a finite, symmetry-reduced model of loop quantum gravity ( LQG) that predicts a "quantum bridge" between contracting and expanding cosmological branches. The distinguishing feature of LQC is the prominent role ...

The Steinhardt–Turok model

In this cyclic model, two parallel

orbifold In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space which is locally a finite group quotient of a Euclidean space. D ...

planes or M-branes collide periodically in a higher-dimensional space. The visible four-dimensional universe lies on one of these branes. The collisions correspond to a reversal from contraction to expansion, or a

followed immediately by a

. The matter and radiation we see today were generated during the most recent collision in a pattern dictated by

quantum fluctuation In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. ...

s created before the branes. After billions of years the universe reached the state we observe today; after additional billions of years it will ultimately begin to contract again.

Dark energy In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the unive ...

corresponds to a force between the branes, and serves the crucial role of solving the monopole,

horizon The horizon is the apparent line that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This line divides all viewing directions based on whether ...

, and flatness problems. Moreover, the cycles can continue indefinitely into the past and the future, and the solution is an

attractor In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain ...

, so it can provide a complete history of the universe. As Richard C. Tolman showed, the earlier cyclic model failed because the universe would undergo inevitable

thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of t ...

heat death. However, the newer cyclic model evades this by having a net expansion each cycle, preventing

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...

from building up. However, there remain major open issues in the model. Foremost among them is that colliding branes are not understood by string theorists, and nobody knows if the

scale invariant In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term ...

spectrum will be destroyed by the big crunch. Moreover, as with

cosmic inflation In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singulari ...

, while the general character of the forces (in the ekpyrotic scenario, a force between branes) required to create the vacuum fluctuations is known, there is no candidate from

particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and ...

The Baum–Frampton model

This more recent cyclic model of 2007 assumes an exotic form of dark energy called

phantom energy Phantom energy is a hypothetical form of dark energy satisfying the equation of state with w < -1. It possesses

negative k ...

, which possesses negative kinetic energy and would usually cause the universe to end in a Big Rip. This condition is achieved if the universe is dominated by dark energy with a cosmological

equation of state In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or intern ...

parameter

w

satisfying the condition

w\equiv \frac <-1

, for

energy density In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or . Often only the ''useful'' or ex ...

and

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...

p. By contrast, Steinhardt–Turok assume

w -1

. In the Baum–Frampton model, a septillionth (or less) of a second (i.e. 10⁻²⁴ seconds or less) before the would-be Big Rip, a turnaround occurs and only one causal patch is retained as our universe. The generic patch contains no

quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All common ...

lepton In particle physics, a lepton is an elementary particle of half-integer spin (spin (physics), spin ) that does not undergo strong interactions. Two main classes of leptons exist: electric charge, charged leptons (also known as the electron-li ...

force carrier In quantum field theory, a force carrier, also known as messenger particle or intermediate particle, is a type of particle that gives rise to forces between other particles. These particles serve as the quanta of a particular kind of physical field. ...

; only

– and its entropy thereby vanishes. The

adiabatic process In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, a ...

of contraction of this much smaller universe takes place with constant vanishing entropy and with no matter including no

black holes A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...

which disintegrated before turnaround. The idea that the universe "comes back empty" is a central new idea of this cyclic model, and avoids many difficulties confronting matter in a contracting phase such as excessive

structure formation In physical cosmology, structure formation is the formation of galaxies, galaxy clusters and larger structures from small early density fluctuations. The universe, as is now known from observations of the cosmic microwave background radiation, beg ...

, proliferation and expansion of

, as well as going through

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states ...

s such as those of QCD and electroweak symmetry restoration. Any of these would tend strongly to produce an unwanted premature bounce, simply to avoid violation of the

second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...

. The condition of

w <-1

may be logically inevitable in a truly infinitely cyclic cosmology because of the entropy problem. Nevertheless, many technical back up calculations are necessary to confirm consistency of the approach. Although the model borrows ideas from string theory, it is not necessarily committed to strings, or to higher dimensions, yet such speculative devices may provide the most expeditious methods to investigate the

internal consistency In statistics and research, internal consistency is typically a measure based on the correlations between different items on the same test (or the same subscale on a larger test). It measures whether several items that propose to measure the same ...

. The value of

w

in the Baum–Frampton model can be made arbitrarily close to, but must be less than, −1.

Other cyclic models

Conformal cyclic cosmology Conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity and proposed by theoretical physicist Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity (i.e. th ...

—a general relativity based theory by

Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus f ...

in which the universe expands until all the matter decays and is turned to light—so there is nothing in the universe that has any time or distance scale associated with it. This permits it to become identical with the Big Bang, so starting the next cycle. *

Loop quantum cosmology Loop quantum cosmology (LQC) is a finite, symmetry-reduced model of loop quantum gravity ( LQG) that predicts a "quantum bridge" between contracting and expanding cosmological branches. The distinguishing feature of LQC is the prominent role ...

which predicts a "quantum bridge" between contracting and expanding cosmological branches.

References

External links

Paul J. Steinhardt
Department of Physics, Princeton University
Paul H. Frampton
Department of Physics and Astronomy, The University of North Carolina at Chapel Hill
Roger Penrose—Cyclical Universe Model
*'
''Pulsating Universe as in Hinduism''
'' {{Authority control Physical cosmology String theory