Loop Quantum Cosmology

By M. Bojowald. Living Reviews in Relativity, 2005

825 citations recorded by the source corpus.

Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/04a11794b33b1fd13b92011c2daa6d0a9f4ddb21

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Citations in the corpus

On the semiclassical limit of 4d spin foam models (2008, background): “This problem has been explored by many authors and from various angles: for example, by the use of semiclassical states [1]–[6], by the extraction of propagators from spin foam models [7]–[9], by numerical simulations [10, 11] and by symmetry reduction [12]–[14].”
Quantum-Spacetime Phenomenology (2008, background): “[126, 92, 127], and references therein, readers can find a list of possible signatures of LQC.”
The pre-inflationary dynamics of loop quantum cosmology: confronting quantum gravity with observations (2012, neutral): “[41] M.”
The Phoenix Project: master constraint programme for loop quantum gravity (2003, methodology): “The author would like to learn about such obstacles and tests in model theories (for instance it is conceivable that Loop Quantum Cosmology [18] provides a fast and interesting test).”
Towards spinfoam cosmology (2010, result): “It can be shown that this choice reproduces the symplectic structures of the LQC variables5 (c, p) or the one of the LQG variables (Eℓ, Uℓ).”
FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY (2005, background): “Also, a c omprehensive review in this field has already appeared [52].”
Loop quantum cosmology of Bianchi type IX models (2009, background): “-m I. INTRODUCTION Loop quantum cosmology (LQC) [1, 2] is an approach to quantum cosmology following the ideas of loop quantum gravity (LQG) [3–5].”
Mathematical structure of loop quantum cosmology (2003, background): “10In the symmetry reduction, one began with the general geometric theory of invariant connections and found that components of a homogeneous connection transform as scalars under gauge transformations [34].”
Loop quantum cosmology of Bianchi I models (2009, methodology): “Loop quantum cosmology (LQC) [4, 5] is constructed by applying methods of LQG to mini-superspaces obtained by a symmetry reduction of general relativity.”
Introduction to Loop Quantum Cosmology (2011, methodology): “As usual in LQC [44], we will compute the holonomies in the fundamental representation of spin 1/2.”