In the 1930s, theoretical physicists, most notably Richard C. Tolman, attempted to make a cyclic model for the universe as an alternative to the Big Bang. These early attempts failed because of the entropy problem that, in statistical mechanics, entropy only increases because of the Second law of thermodynamics. 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. Richard Chace Tolman (March 4, 1881–September 5, 1948) was an American mathematical physicist and physical chemist who was an authority on statistical mechanics and made important contributions to the early development of theoretical cosmology. ... According to the Big Bang model, the universe developed from an extremely dense and hot state. ... The second law of thermodynamics is an expression of the universal law of increasing entropy. ... In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. ...

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. Brane cosmology is a protoscience motivated by, but not rigorously derived from, superstring theory and M-theory. ... According to the Big Bang model, the universe developed from an extremely dense and hot state. ... The ekpyrotic universe or ekpyrotic scenario is a cosmological theory of the origin of the universe. ... Year 2001 (MMI) was a common year starting on Monday (link displays the 2001 Gregorian calendar). ... Paul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. ... Princeton University is a private coeducational research university located in Princeton, New Jersey, in the United States of America. ... Neil Geoffrey Turok (1967) is a South African cosmologist. ... The University of Cambridge is the second-oldest university in the English-speaking world, with one of the most selective sets of entry requirements in the United Kingdom. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. ... According to the Big Bang model, the universe developed from an extremely dense and hot state. ...

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. Phantom energy is a hypothetical form of dark energy with equation of state . ... Paul Frampton, Rubin Distinguished Professor. ... The University of North Carolina at Chapel Hill is a public, coeducational, research university located in Chapel Hill, North Carolina, United States. ...

The Steinhardt-Turok model

In this cyclic model, two parallel orbifold 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. In topology and group theory, an orbifold (for orbit-manifold) is a generalization of a manifold. ... This article or section is in need of attention from an expert on the subject. ... P-branes or branes are terms from quantum superstring theory used to refer to membrane-like structures of one to eleven dimensions that arise in equations of this heavily mathematical theory. ... This article is about the cosmological theory. ... According to the Big Bang model, the universe developed from an extremely dense and hot state. ... In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. ... In physics, magnetic monopole is a term describing a hypothetical particle that could be quickly clarified to a person familiar with magnets but not electromagnetic theory as a magnet with only one pole. In more accurate terms, it would have net magnetic charge. Interest in the concept stems from particle... This article does not cite any references or sources. ... The flatness problem is a cosmological problem with the Big Bang theory, which is solved by hypothesising an inflationary universe. ... In dynamical systems, an attractor is a set to which the system evolves after a long enough time. ...

The earlier cyclic model of Richard C. Tolman failed because the universe would undergo inevitable thermodynamic heat death. However, the 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, or even what happens when two branes collide. 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. Moreover, the scenario uses some essential ideas from string theory, principally extra dimensions, branes and orbifolds. String theory itself is a controversial idea in physics. Richard Chace Tolman (March 4, 1881–September 5, 1948) was an American mathematical physicist and physical chemist who was an authority on statistical mechanics and made important contributions to the early development of theoretical cosmology. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... The heat death is a possible final state of the universe, in which it has reached maximum entropy. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... This article or section is in need of attention from an expert on the subject. ... In physics, scale invariance is the feature of physical objects of laws that do not change if the space is magnified, i. ... In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density. ... The ekpyrotic universe or ekpyrotic scenario is a cosmological theory of the origin of the universe. ... In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... In physics, Kaluza-Klein theory (or KK theory, for short) is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. ... In topology and group theory, an orbifold (for orbit-manifold) is a generalization of a manifold. ...

Originally, ekpyrotic models described two branes separated along a fifth dimension which collide once. Crucially, both the ekpyrotic and cyclic models create the fluctuations we observe today in a contracting "ekpyrotic" phase. However, in the ekpyrotic model, while a future collision with a different brane could conceivably happen in the future, ending our epoch in a conflagration, this happens randomly, not periodically. There were problems with the old ekpyrotic picture having to do with the very special, nearly supersymmetric initial state required in order to end up with a nearly homogeneous universe: the problems solved by cosmic inflation, such as the monopole, flatness and homogeneity problems were shifted to a set of fine-tuned initial conditions. The ekpyrotic picture was not connected to the issue of dark energy. In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... In particle physics, supersymmetry is a hypothetical symmetry that relates bosons and fermions. ... In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density. ... Fine Tuning is the name of XM Satellite Radios eclectic music channel. ... In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ... In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. ...

There are other technical differences having to do with the nature of the branes. For example, in the ekpyrotic model, they are D-branes; while in the cyclic model, they are orbifold planes. In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ... In topology and group theory, an orbifold (for orbit-manifold) is a generalization of a manifold. ...

The Baum-Frampton model

This more recent cyclic model of 2006 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 which is phantom energy throughout a cycle, including at present. (By contrast, Steinhardt-Turok assume w is never less than -1.) In the Baum-Frampton model, a trillion-trillionth (or less) of a second before the would-be Big Rip a turnaround occurs and only one causal patch is retained as our universe. This patch contains no quarks or leptons, only dark energy and a tiny number of extremely low-energy photons. Its entropy therefore essentially 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. Phantom energy is a hypothetical form of dark energy with equation of state . ... The Big Rip is a cosmological hypothesis about the ultimate fate of the Universe, in which the elements of the universe, from galaxies to atoms, are progressively torn apart by the expansion of the universe. ... The six flavours of quarks and their most likely decay modes. ... In physics, a particle is a lepton if it has a spin of 1/2 and does not experience the strong nuclear force. ... In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... In thermodynamics, an adiabatic process or an isocaloric process is a process in which no heat is transferred to or from the working fluid. ... This article is about the astronomical body. ...

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 in reverse through phase transitions such as recombination, QCD and electroweak transitions. 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 still 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, although such speculative devices may well also 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. It has been suggested that this article or section be merged into Large-scale structure of the cosmos. ... This article is about the astronomical body. ... In physics, a phase transition, (or phase change) is the transformation of a thermodynamic system from one phase to another. ... The second law of thermodynamics is an expression of the universal law of increasing entropy. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... Higher dimension in mathematics refers to any number of dimensions greater than three. ... Internal consistency, in gaming, refers to the consistency of the physical and social rules that affect online computer role-playing games. ...

Distinguishing models

The Planck Surveyor mission should provide a measurement of w to unprecedented accuracy, discover whether w < -1 or not, and thereby discriminate between the models. WMAP image, unrelated to Planck The Planck Surveyor is the third Medium-Sized Mission (M3) of ESAs Horizon 2000 Scientific Programme. ...

See also

• Tolman, R.C. (1934). Relativity, Thermodynamics, and Cosmology. Oxford: Clarendon Press. LCCN 340-32023.  Reissued (1987) New York: Dover ISBN 0-486-65383-8.
• Cosmological constant
• Lauris Baum and Paul H. Frampton, Phys. Rev. Lett. 98, 071301 (2007).

The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. ...

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
• Simplified Overview Comparing Standard and Ekpyrotic Models of the Universe

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