Cyclic model
Encyclopedia
A cyclic model is any of several cosmological models in which the universe
follows infinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by Albert Einstein
in 1930 theorized a universe following an eternal
series of oscillations, each beginning with a big bang
and ending with a big crunch
; 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
.
, 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 entropy problem: according to the Second Law of Thermodynamics
, 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
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 a brane cosmology
model of the creation of the universe
, derived from the earlier ekpyrotic
model. It was proposed in 2001 by Paul Steinhardt
of Princeton University
and Neil Turok
of Cambridge University. The theory describes a universe exploding into existence not just once, but repeatedly over time. The theory could potentially explain why a mysterious repulsive form of energy known as the "cosmological constant
", and which is accelerating the expansion of the universe, is several orders of magnitude smaller than predicted by the standard Big Bang
model.
A different cyclic model relying on the notion of phantom energy
was proposed in 2007 by Lauris Baum and Paul Frampton
of the University of North Carolina at Chapel Hill
.
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 big crunch
followed immediately by a big bang
. The matter and radiation we see today were generated during the most recent collision in a pattern dictated by quantum fluctuations created before the branes. Eventually, the universe reached the state we observe today, before beginning to contract again many billions of years in the future. Dark energy
corresponds to a force between the branes, and serves the crucial role of solving the monopole, horizon
, and flatness problems. Moreover the cycles can continue indefinitely into the past and the future, and the solution is an attractor
, 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
heat death. However, the newer cyclic model evades this by having a net expansion each cycle, preventing entropy
from building up. However, there are major problems with the model. Foremost among them is that colliding branes
are not understood by string theorists, and nobody knows if the scale invariant
spectrum will be destroyed by the big crunch. Moreover, like cosmic inflation
, 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
.
) throughout a cycle, including at present. (By contrast, Steinhardt–Turok assume w is never less than −1.) In the Baum–Frampton model, a septillionth (or less) of a second 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
, lepton
or force carrier
; only dark energy
– and its entropy thereby vanishes. The adiabatic process
of contraction of this much smaller universe takes place with constant vanishing entropy and with no matter including no black holes 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
, proliferation and expansion of black holes, as well as going through phase transition
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 surprising w < −1 condition 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
. The value of w in the Baum–Frampton model can be made arbitrarily close to, but must be less than, −1.
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Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
follows infinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
in 1930 theorized a universe following an eternal
Eternity
While in the popular mind, eternity often simply means existence for a limitless amount of time, many have used it to refer to a timeless existence altogether outside time. By contrast, infinite temporal existence is then called sempiternity. Something eternal exists outside time; by contrast,...
series of oscillations, each beginning with a big bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
and ending with a big crunch
Big Crunch
In physical cosmology, the Big Crunch is one possible scenario for the ultimate fate of the universe, in which the metric expansion of space eventually reverses and the universe recollapses, ultimately ending as a black hole singularity.- Overview :...
; in the interim, the universe would expand
Metric expansion of space
The metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...
for a period of time before the gravitational attraction of matter causes it to collapse back in and undergo a bounce
Big Bounce
The Big Bounce is a theoretical scientific model of the formation of the known universe. It is implied by the cyclic model or oscillatory universe interpretation of the Big Bang where the first cosmological event was the result of the collapse of a previous universe.- Expansion and contraction...
.
Overview
In the 1930s, theoretical physicists, most notably Albert EinsteinAlbert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
, considered the possibility of a cyclic model for the universe as an (everlasting) alternative to the model of an expanding universe
Metric expansion of space
The metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...
. However, work by Richard C. Tolman
Richard C. Tolman
Richard Chace Tolman was an American mathematical physicist and physical chemist who was an authority on statistical mechanics. He also made important contributions to theoretical cosmology in the years soon after Einstein's discovery of general relativity...
in 1934 showed that these early attempts failed because of the entropy problem: according to the Second Law of Thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
, 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
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
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 a brane cosmology
Brane cosmology
Brane cosmology refers to several theories in particle physics and cosmology motivated by, but not exclusively derived from, superstring theory and M-theory.-Brane and bulk:...
model of the creation of the universe
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
, derived from the earlier ekpyrotic
Ekpyrotic
The ekpyrotic universe, or ekpyrotic scenario, is a cosmological model of the origin and shape of the universe. The name comes from a Stoic term ekpyrosis meaning conflagration or in Stoic usage "conversion into fire"...
model. It was proposed in 2001 by Paul Steinhardt
Paul Steinhardt
Paul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. He received his B.S. at the California Institute of Technology and his Ph.D. in Physics at Harvard University...
of Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
and Neil Turok
Neil Turok
Neil Geoffrey Turok is the Director of Perimeter Institute for Theoretical Physics. He is the son of Mary and Ben Turok, activists in the anti-apartheid movement and the African National Congress.-Career:...
of Cambridge University. The theory describes a universe exploding into existence not just once, but repeatedly over time. The theory could potentially explain why a mysterious repulsive form of energy known as the "cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
", and which is accelerating the expansion of the universe, is several orders of magnitude smaller than predicted by the standard Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
model.
A different cyclic model relying on the notion of phantom energy
Phantom energy
Phantom energy is a hypothetical form of dark energy with equation of state \! w Phantom energy is a hypothetical form of dark energy with equation of state...
was proposed in 2007 by Lauris Baum and Paul Frampton
Paul Frampton
Paul Frampton is a particle phenomenologist.Since 1996, he is the Louis D. Rubin, Jr. Distinguished Professor of physics and astronomy, at the University of North Carolina...
of the University of North Carolina at Chapel Hill
University of North Carolina at Chapel Hill
The University of North Carolina at Chapel Hill is a public research university located in Chapel Hill, North Carolina, United States...
.
The Steinhardt–Turok model
In this cyclic model, two parallel orbifoldOrbifold
In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold...
planes or M-branes
Membrane (M-Theory)
In theoretical physics, a membrane, brane, or p-brane is a spatially extended mathematical concept that appears in string theory and related theories...
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 big crunch
Big Crunch
In physical cosmology, the Big Crunch is one possible scenario for the ultimate fate of the universe, in which the metric expansion of space eventually reverses and the universe recollapses, ultimately ending as a black hole singularity.- Overview :...
followed immediately by a big bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
. The matter and radiation we see today were generated during the most recent collision in a pattern dictated by quantum fluctuations created before the branes. Eventually, the universe reached the state we observe today, before beginning to contract again many billions of years in the future. Dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
corresponds to a force between the branes, and serves the crucial role of solving the monopole, horizon
Horizon problem
The horizon problem is a problem with the standard cosmological model of the Big Bang which was identified in the 1970s. It points out that different regions of the universe have not "contacted" each other because of the great distances between them, but nevertheless they have the same temperature...
, and flatness problems. Moreover the cycles can continue indefinitely into the past and the future, and the solution is an attractor
Attractor
An attractor is a set towards which a dynamical system evolves over time. That is, points that get close enough to the attractor remain close even if slightly disturbed...
, so it can provide a complete history of the universe.
As Richard C. Tolman
Richard C. Tolman
Richard Chace Tolman was an American mathematical physicist and physical chemist who was an authority on statistical mechanics. He also made important contributions to theoretical cosmology in the years soon after Einstein's discovery of general relativity...
showed, the earlier cyclic model failed because the universe would undergo inevitable thermodynamic
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
heat death. However, the newer cyclic model evades this by having a net expansion each cycle, preventing entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
from building up. However, there are major problems with the model. Foremost among them is that colliding branes
Membrane (M-Theory)
In theoretical physics, a membrane, brane, or p-brane is a spatially extended mathematical concept that appears in string theory and related theories...
are not understood by string theorists, and nobody knows if the scale invariant
Scale invariance
In physics and mathematics, 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...
spectrum will be destroyed by the big crunch. Moreover, like cosmic inflation
Cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...
, while the general character of the forces (in the ekpyrotic
Ekpyrotic
The ekpyrotic universe, or ekpyrotic scenario, is a cosmological model of the origin and shape of the universe. The name comes from a Stoic term ekpyrosis meaning conflagration or in Stoic usage "conversion into fire"...
scenario, a force between branes) required to create the vacuum fluctuations is known, there is no candidate from particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
.
The Baum–Frampton model
This more recent cyclic model of 2007 makes a different technical assumption concerning the equation of state of the dark energy which relates pressure and density through a parameter w. It assumes w < −1 (a condition called phantom energyPhantom energy
Phantom energy is a hypothetical form of dark energy with equation of state \! w Phantom energy is a hypothetical form of dark energy with equation of state...
) throughout a cycle, including at present. (By contrast, Steinhardt–Turok assume w is never less than −1.) In the Baum–Frampton model, a septillionth (or less) of a second before the would-be Big Rip
Big Rip
The Big Rip is a cosmological hypothesis first published in 2003, about the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, is progressively torn apart by the expansion of the universe at a certain time in the future...
, a turnaround occurs and only one causal patch is retained as our universe. The generic patch contains no quark
Quark
A quark is an 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. Due to a phenomenon known as color confinement, quarks are never directly...
, lepton
Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
or force carrier
Force carrier
In particle physics, quantum field theories such as the Standard Model describe nature in terms of fields. Each field has a complementary description as the set of particles of a particular type...
; only dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
– and its entropy thereby vanishes. The adiabatic process
Adiabatic process
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
of contraction of this much smaller universe takes place with constant vanishing entropy and with no matter including no black holes 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
Structure formation
Structure formation refers to a fundamental problem in physical cosmology. The universe, as is now known from observations of the cosmic microwave background radiation, began in a hot, dense, nearly uniform state approximately 13.7 Gyr ago...
, proliferation and expansion of black holes, as well as going through phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
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
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
. The surprising w < −1 condition 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
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
, 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
Internal consistency
In statistics and research, internal consistency is typically a measure based on the correlations between different items on the same test . It measures whether several items that propose to measure the same general construct produce similar scores...
. The value of w in the Baum–Frampton model can be made arbitrarily close to, but must be less than, −1.
The Mills model
In the 1990's Randell Mills, author of "The Grand Unified Theory of Classical Physics," predicted a cyclic-model along with the acceleration of the expansion of the universe. In his book Mills calculates the period of the cycle to be 9.83x10^11 years.See also
- CosmologyCosmologyCosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
- Richard Tolman
- Big BounceBig BounceThe Big Bounce is a theoretical scientific model of the formation of the known universe. It is implied by the cyclic model or oscillatory universe interpretation of the Big Bang where the first cosmological event was the result of the collapse of a previous universe.- Expansion and contraction...
- Cosmological constantCosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
- Conformal Cyclic CosmologyConformal Cyclic CosmologyThe Conformal Cyclic Cosmology is a cosmological model in the framework of general relativity, advanced by the theoretical physicist Sir Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big...
- Cycles of time in Hinduism
Further reading
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- R. H. Dicke, P. J. E. Peebles, P. G. Roll and D. T. Wilkinson, "Cosmic Black-Body Radiation," Astrophysical Journal 142 (1965), 414. This paper discussed the oscillatory universe as one of the main cosmological possibilities of the time.
- S. W. Hawking and G. F. R. Ellis, The large-scale structure of space-time (Cambridge, 1973).
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
- Cyclic universe on arxiv.org
- "The Cyclic Universe": A Talk with Neil Turok
- Roger Penrose - Cyclical Universe Model
- "The Grand Unified Theory of Classical Physics, Part 3: Cosmology"