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Loop quantum cosmology
, 2006
"... 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 spacetime inevitably comes to an end after a ..."
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Cited by 48 (11 self)
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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 spacetime 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 spacetime 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 spacetime 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 spacetime arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.
Reconstructing the Universe
, 2005
"... We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a largescale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a f ..."
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Cited by 23 (2 self)
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We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a largescale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time.
Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
"... Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completel ..."
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Cited by 12 (5 self)
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Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric models. This then presents a further consistency check of the whole scheme in inhomogeneous situations, lending further credence to the physical results obtained so far mainly in homogeneous models. New applications in particular of the spherically symmetric model in the context of black hole physics are discussed. 1
Testing Lorentz invariance violation in quantum gravity theories,” arXiv:grqc/0502093
"... Much research has been done in the latter years on the subject of Lorentz violation induced by Quantum Gravity effects. On the theoretical side it has been shown that both Loop Quantum Gravity and String Theory predict that Lorentz violation can be induced at an energy near to the Planck scale. On t ..."
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Cited by 6 (0 self)
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Much research has been done in the latter years on the subject of Lorentz violation induced by Quantum Gravity effects. On the theoretical side it has been shown that both Loop Quantum Gravity and String Theory predict that Lorentz violation can be induced at an energy near to the Planck scale. On the other hand, most of the experimental results in the latter years, have confirmed that the laws of physics are Lorentz invariant at low energy with very high accuracy. The inclusion of one and twoloop contributions from a Lorentz violating Lagrangian dramatically change the above picture: the loop momenta run into the Planck scale and above and from the ”divergent ” terms finite Lorentz violating contributions of order one arise. These can be suppressed through suitable counterterms in the Lagrangian, originating a strong fine tuning problem. A brief discussion of these issues and their possible influence in future research follows.
Conserved Topological Defects in NonEmbedded Graphs in Quantum Gravity
"... We follow up on previous work which found that commonly used graph evolution moves lead to conserved quantities that can be expressed in terms of the braiding of the graph in its embedding space. We study nonembedded graphs under three distinct sets of dynamical rules and find nontrivial conserved ..."
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We follow up on previous work which found that commonly used graph evolution moves lead to conserved quantities that can be expressed in terms of the braiding of the graph in its embedding space. We study nonembedded graphs under three distinct sets of dynamical rules and find nontrivial conserved quantities that can be expressed in terms of topological defects in the dual geometry. For graphs dual to 2dimensional simplicial complexes we identify all the conserved quantities of the evolution. We also indicate expected
The perturbative Reggecalculus regime of loop quantum gravity
 Nuclear Physics B 796 [FS] (2008) 581–621. BOJAN MOHAR AND IGOR RIVIN
"... The relation between Loop Quantum Gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the BarrettCrane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of Loop Quantum Gra ..."
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The relation between Loop Quantum Gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the BarrettCrane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of Loop Quantum Gravity and show that it admits an effective description in terms of perturbative areaReggecalculus. The regime of interest is identified by a class of states given by superpositions of fourvalent spin networks, peaked on large spins. As a probe of the dynamics in this regime, we compute explicitly two and threearea correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in areaReggecalculus with a single 4simplex, once a specific perturbative action and measure have been chosen in the Reggecalculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed. 1
Higher curvature counter terms cause the bounce in loop cosmology
"... Abstract. In the loop approach to the quantisation of gravity, one uses a Hilbert space which is too singular for some operators to be realised as derivatives. This is usually addressed by instead using finite difference operators at the Planck scale, a process known as “polymerisation”. In the symm ..."
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Abstract. In the loop approach to the quantisation of gravity, one uses a Hilbert space which is too singular for some operators to be realised as derivatives. This is usually addressed by instead using finite difference operators at the Planck scale, a process known as “polymerisation”. In the symmetry reduced example of loop cosmology, we study an ambiguity in the regularisation which we relate to the ambiguity of fixing the coefficients of infinitely many higher curvature counter terms augmenting the EinsteinHilbert action. Thus the situation is comparable to he one in a naive perturbative treatment of quantum gravity with a cutoff where the necessary presence of infinitely many higher derivative terms compromises predictability. As a byproduct, we demonstrate in an appendix that it is possible to have higher curvature actions for gravity which still lead to first order equations of motion like in the Friedmann case. Preprint LMUASC 58/09 1.