Conformal Cyclic Cosmology
Encyclopedia
The Conformal Cyclic Cosmology (CCC) 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 Bang
singularity of the next. Penrose outlines this theory in his 2010 book Cycles of Time: An Extraordinary New View of the Universe
.
followed by an infinite future expansion. Penrose noticed that the past conformal boundary of one copy of FLRW spacetime can be "attached" to the future conformal boundary of another, after an appropriate conformal rescaling
. In particular, each individual FLRW metric
is multiplied by the square of a conformal factor 
that approaches zero at timelike infinity
, effectively "squashing down" the future conformal boundary to a conformally regular hypersurface
(which is spacelike if there is a positive cosmological constant
, as we currently believe). The result is a new solution to Einstein's equations, which Penrose takes to represent the entire Universe, and which is composed of a sequence of sectors that Penrose calls "aeons."
obey the laws of conformally invariant quantum theory
, they will behave in the same way in the rescaled aeons as in the original FLRW counterparts. (Classically, this corresponds to the fact that light cone structure is preserved under conformal rescalings.) For such particles, the boundary between aeons is not a boundary at all, but just a spacelike surface that can be passed across like any other. Fermions, on the other hand, remain confined to a given aeon. This provides a convenient solution to the black hole information paradox
; according to Penrose, fermions must be irreversibly converted into radiation during black hole evaporation, to preserve the smoothness of the boundary between aeons.
The curvature properties of Penrose's cosmology are also highly desirable. First, the boundary between aeons satisfies the Weyl curvature hypothesis
, thus providing a certain kind of low-entropy past as required by statistical mechanics and by observation. Second, Penrose has calculated that a certain amount of gravitational radiation should be preserved across the boundary between aeons. Penrose suggests this extra gravitational radiation may be enough to explain the observed cosmic acceleration without appeal to a dark energy
matter field.
of a paper claiming that observations of the cosmic microwave background made by the Wilkinson Microwave Anisotropy Probe
and the BOOMERanG experiment
showed concentric anomalies which were consistent with the CCC hypothesis, with a low probability of the null hypothesis
that the observations in question were caused by chance. However, the statistical significance of the claimed detection has since been questioned. Three groups have independently attempted to reproduce these results, but found that the detection of the concentric anomalies was not statistically significant, in the sense that such circles would appear in a proper Gaussian simulation of the anisotropy in the CMB data. Penrose and Gurzadyan responded that, while the presence of individual circles in the CMB data was not statistically significant, they claim to have found concentric families of circles, the presence of which cannot be found in the random Gaussian simulation of the data.
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, advanced by the theoretical physicist Sir Roger Penrose
Roger Penrose
Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...
. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the 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...
singularity of the next. Penrose outlines this theory in his 2010 book Cycles of Time: An Extraordinary New View of the Universe
Cycles of Time (book)
Cycles of Time: An Extraordinary New View of the Universe is a science book by mathematical physicist Roger Penrose published by The Bodley Head in 2010...
.
Basic construction
Penrose's basic construction is to connect together a countable sequence of open FLRW spacetimes, each representing a big bangBig 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...
followed by an infinite future expansion. Penrose noticed that the past conformal boundary of one copy of FLRW spacetime can be "attached" to the future conformal boundary of another, after an appropriate conformal rescaling
Conformal map
In mathematics, a conformal map is a function which preserves angles. In the most common case the function is between domains in the complex plane.More formally, a map,...
. In particular, each individual FLRW metric
is multiplied by the square of a conformal factor that approaches zero at timelike infinityPenrose diagram
In theoretical physics, a Penrose diagram is a two-dimensional diagram that captures the causal relations between different points in spacetime...
, effectively "squashing down" the future conformal boundary to a conformally regular hypersurface
Hypersurface
In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface...
(which is spacelike if there is a positive 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...
, as we currently believe). The result is a new solution to Einstein's equations, which Penrose takes to represent the entire Universe, and which is composed of a sequence of sectors that Penrose calls "aeons."
Physical implications
The significant feature of this construction for particle physics is that, since bosonsBoson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
obey the laws of conformally invariant quantum theory
Conformal field theory
A conformal field theory is a quantum field theory that is invariant under conformal transformations...
, they will behave in the same way in the rescaled aeons as in the original FLRW counterparts. (Classically, this corresponds to the fact that light cone structure is preserved under conformal rescalings.) For such particles, the boundary between aeons is not a boundary at all, but just a spacelike surface that can be passed across like any other. Fermions, on the other hand, remain confined to a given aeon. This provides a convenient solution to the black hole information paradox
Black hole information paradox
The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state...
; according to Penrose, fermions must be irreversibly converted into radiation during black hole evaporation, to preserve the smoothness of the boundary between aeons.
The curvature properties of Penrose's cosmology are also highly desirable. First, the boundary between aeons satisfies the Weyl curvature hypothesis
Weyl curvature hypothesis
The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Sir Roger Penrose in an article in 1979 in an attempt to provide explanations for two of the...
, thus providing a certain kind of low-entropy past as required by statistical mechanics and by observation. Second, Penrose has calculated that a certain amount of gravitational radiation should be preserved across the boundary between aeons. Penrose suggests this extra gravitational radiation may be enough to explain the observed cosmic acceleration without appeal to a 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...
matter field.
Empirical tests
In 2010, Penrose and V. G. Gurzadyan published a preprintPreprint
A preprint is a draft of a scientific paper that has not yet been published in a peer-reviewed scientific journal.-Role:Publication of manuscripts in a peer-reviewed journal often takes weeks, months or even years from the time of initial submission, because manuscripts must undergo extensive...
of a paper claiming that observations of the cosmic microwave background made by the Wilkinson Microwave Anisotropy Probe
Wilkinson Microwave Anisotropy Probe
The Wilkinson Microwave Anisotropy Probe — also known as the Microwave Anisotropy Probe , and Explorer 80 — is a spacecraft which measures differences in the temperature of the Big Bang's remnant radiant heat — the Cosmic Microwave Background Radiation — across the full sky. Headed by Professor...
and the BOOMERanG experiment
BOOMERanG experiment
The BOOMERanG experiment measured the cosmic microwave background radiation of a part of the sky during three sub-orbital balloon flights. It was the first experiment to make large, high fidelity images of the CMB temperature anisotropies...
showed concentric anomalies which were consistent with the CCC hypothesis, with a low probability of the null hypothesis
Null hypothesis
The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position...
that the observations in question were caused by chance. However, the statistical significance of the claimed detection has since been questioned. Three groups have independently attempted to reproduce these results, but found that the detection of the concentric anomalies was not statistically significant, in the sense that such circles would appear in a proper Gaussian simulation of the anisotropy in the CMB data. Penrose and Gurzadyan responded that, while the presence of individual circles in the CMB data was not statistically significant, they claim to have found concentric families of circles, the presence of which cannot be found in the random Gaussian simulation of the data.
See also
- Conformal geometryConformal geometryIn mathematics, conformal geometry is the study of the set of angle-preserving transformations on a space. In two real dimensions, conformal geometry is precisely the geometry of Riemann surfaces...
- Cyclic modelCyclic modelA 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...
- Black hole information paradoxBlack hole information paradoxThe black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state...
- White holeWhite holeA white hole, in general relativity, is a hypothetical region of spacetime which cannot be entered from the outside, but from which matter and light may escape. In this sense it is the reverse of a black hole, which can be entered from the outside, but from which nothing, including light, may escape...
- Cycles of Time: An Extraordinary New View of the UniverseCycles of Time (book)Cycles of Time: An Extraordinary New View of the Universe is a science book by mathematical physicist Roger Penrose published by The Bodley Head in 2010...