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quantum cosmology Quantum cosmology is the attempt in theoretical physics to develop a quantum theory of the universe. This approach attempts to answer open questions of classical physical cosmology, particularly those related to the first phases of the universe. ...
(LQC)612.01236Loop Quantum Cosmology: A brief review">002.05703Critical evaluation of common claims in loop quantum cosmology">612.04551Testing loop quantum cosmology">703.10274Loop quantum cosmology and singularities">906.01501Effective Field Theory of Loop Quantum Cosmology"> is a
finite Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...
,
symmetry Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
-reduced model of
loop quantum gravity Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attem ...
( LQG) that predicts a "quantum bridge" between contracting and expanding
cosmological Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
branches. The distinguishing feature of LQC is the prominent role played by the
quantum geometry In theoretical physics, quantum geometry is the set of mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at distance scales comparable to the Planck length. At these d ...
effects of loop quantum gravity (LQG). In particular,
quantum geometry In theoretical physics, quantum geometry is the set of mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at distance scales comparable to the Planck length. At these d ...
creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction and thereby resolving singularities of general relativity. Once singularities are resolved, the conceptual paradigm of
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...
changes and one has to revisit many of the standard issues—e.g., the "
horizon problem The horizon problem (also known as the homogeneity problem) is a cosmological fine-tuning problem within the Big Bang model of the universe. It arises due to the difficulty in explaining the observed homogeneity of causally disconnected region ...
"—from a new perspective. Since LQG is based on a specific quantum theory of
Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to poin ...
, geometric observables display a fundamental discreteness that play a key role in
quantum dynamics In physics, quantum dynamics is the quantum version of classical dynamics. Quantum dynamics deals with the motions, and energy and momentum exchanges of systems whose behavior is governed by the laws of quantum mechanics. Quantum dynamics is relevan ...
: While predictions of LQC are very close to those of quantum
geometrodynamics In theoretical physics, geometrodynamics is an attempt to describe spacetime and associated phenomena completely in terms of geometry. Technically, its goal is to grand unification, unify the fundamental forces and reformulate general relativity ...
(QGD) away from the Planck regime, there is a dramatic difference once densities and curvatures enter the Planck scale. In LQC the
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 the ...
is replaced by a
quantum bounce The Big Bounce is a hypothesized cosmological model for the origin of the known universe. It was originally suggested as a phase of the ''cyclic model'' or ''oscillatory universe'' interpretation of the Big Bang, where the first cosmological ev ...
. Study of LQC has led to many successes, including the emergence of a possible mechanism for
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 singularity ...
, resolution of
gravitational singularities A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is so intense that spacetime itself breaks down catastrophically. As such, a singularity is by definition no longer part of the regular sp ...
, as well as the development of effective semi-classical Hamiltonians. This subfield originated in 1999 by
Martin Bojowald Martin Bojowald (born 18 February 1973 in Jülich) is a German physicist who now works on the faculty of the Penn State Physics Department, where he is a member of the Institute for Gravitation and the Cosmos. Prior to joining Penn State he spent ...
, and further developed in particular by
Abhay Ashtekar Abhay Vasant Ashtekar (born 5 July 1949) is an Indian theoretical physicist. He is the Eberly Professor of Physics and the Director of the Institute for Gravitational Physics and Geometry at Pennsylvania State University. As the creator of As ...
and
Jerzy Lewandowski Jerzy Lewandowski is a Polish theoretical physicist who studies quantum gravity. He is a professor of physics at the University of Warsaw. Lewandowski received his doctorate in Warsaw under Andrzej Trautman. He worked closely with Abhay Ashtekar a ...
, as well as
Tomasz Pawłowski Tomasz is a Polish given name, the equivalent of Thomas in English. Notable people with the given name include: *Tomasz Adamek (born 1976), Polish heavyweight boxer *Tomasz Arciszewski (1877–1955), Polish socialist politician and Prime Minist ...
and Parampreet Singh, et al. In late 2012 LQC represented a very active field in
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, with about three hundred papers on the subject published in the literature. There has also recently been work by Carlo Rovelli, et al. on relating LQC to
spinfoam In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity. These structu ...
cosmology. However, the results obtained in LQC are subject to the usual restriction that a truncated classical theory, then quantized, might not display the true behaviour of the full theory due to artificial suppression of degrees of freedom that might have large quantum fluctuations in the full theory. It has been argued that singularity avoidance in LQC are by mechanisms only available in these restrictive models and that singularity avoidance in the full theory can still be obtained but by a more subtle feature of LQG.


Big bounce in loop quantum cosmology

Due to the quantum geometry, the Big Bang is replaced by a big bounce without any assumptions on the matter content or any fine tuning. An important feature of loop quantum cosmology is the effective
space-time In physics, spacetime is a mathematical model that combines the three-dimensional space, three dimensions of space and one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visualize S ...
description of the underlying quantum evolution. The effective dynamics approach has been extensively used in loop quantum cosmology to describe physics at the Planck scale and the very early universe. Rigorous numerical simulations have confirmed the validity of the effective dynamics, which provides an excellent approximation to the full loop quantum dynamics. It has been shown that only when the states have very large quantum fluctuations at late times, which means that they do not lead to macroscopic universes as described by general relativity, that the effective dynamics has departures from the quantum dynamics near bounce and the subsequent evolution. In such a case, the effective dynamics overestimates the density at the bounce, but still captures the qualitative aspects extremely well.


Scale-invariant loop quantum cosmology

If the underlying spacetime geometry with matter has a
scale invariance 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 ...
, which has been proposed to resolve the
problem of time In theoretical physics, the problem of time is a conceptual conflict between general relativity and quantum mechanics in that quantum mechanics regards the flow of time as universal and absolute, whereas general relativity regards the flow of tim ...
, Immirzi ambiguity and hierarchy problem of fundamental couplings, then the resulting loop quantum geometry has no definitive discrete gaps or a minimum size. Consequently, in scale-invariant LQC, the Big Bang is shown not to be replaced by a quantum bounce.


See also

* * * *
Canonical quantum gravity In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity (or canonical gravity). It is a Hamiltonian formulation of Einstein's general theory of relativity. The basic theory was outlined by B ...
*
Dilaton In particle physics, the hypothetical dilaton particle is a particle of a scalar field \varphi that appears in theories with extra dimensions when the volume of the compactified dimensions varies. It appears as a radion in Kaluza–Klein theor ...


References

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External links


Loop quantum cosmology on arxiv.orgQuantum Nature of The Big Bang in Loop Quantum CosmologyGravity and the QuantumLoop Quantum Cosmology, Martin BojowaldAbhay Ashtekar, Parampreet Singh "Loop Quantum Cosmology: A Status Report"
Physical cosmology Loop quantum gravity