Discreteness corrections and higher spatial derivatives in effective canonical quantum gravity

Bojowald, Martin; Paily, George M.; Reyes, Juan D.

doi:10.1103/physrevd.90.025025

Cited by 38 publications

(77 citation statements)

References 62 publications

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“…A possible solution to this problem is to implement holonomy modifications in an anomaly-free way which does not break any gauge transformations but may deform the classical structure of hypersurface deformations given in [63,64]. Consistent deformations are possible in spherically symmetric models with holonomy modifications [71,72,73,74,75,76,77], but they imply a non-classical space-time structure which is related to slicing independence only in some cases, and after field redefinitions [78,79]. The latter feature not only resolves the contradiction between holonomy modifications and covariance pointed out in [11], it also shows why singularities can be resolved in loop quantum cosmology even for matter obeying the usual energy conditions: Not only the dynamics but also space-time structure become non-classical as a consequence of holonomy modifications, unhinging the mathematical foundation of singularity theorems.…”

Section: Covariancementioning

confidence: 99%

Critical Evaluation of Common Claims in Loop Quantum Cosmology

Bojowald

2020

Universe

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A large number of models have been analyzed in loop quantum cosmology, using mainly minisuperspace constructions and perturbations. At the same time, general physics principles from effective field theory and covariance have often been ignored. A consistent introduction of these ingredients requires substantial modifications of existing scenarios. As a consequence, none of the broader claims made mainly by the Ashtekar school -such as the genericness of bounces with astonishingly semiclassical dynamics, robustness with respect to quantization ambiguities, the realization of covariance, and the relevance of certain technical results for potential observations -hold up to scrutiny. Several useful lessons for a sustainable version of quantum cosmology can be drawn from this outcome. * e-mail address: bojowald@gravity.psu.edu 1 All quotations from [1] given in this paper refer to the second preprint version.

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Section: Covariancementioning

confidence: 99%

Critical Evaluation of Common Claims in Loop Quantum Cosmology

Bojowald

2020

Universe

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“…A generic modification which does not require a specific value of γ can be obtained for the theories considered here, as has been known for some time for real variables [1,5]. Since the Hamiltonian constraint in real variables has the same form as the general spherically symmetric constraint in gauge-invariant variables, the same modification can be transferred also to self-dual type variables (γ 2 = ǫ) provided we implement it at the gauge-invariant level.…”

Section: Modified Bracketsmentioning

confidence: 96%

“…This modification, following [1,5], differs from the modification of [20] in that it modifies not only the constraints but also their brackets (while the latter remain closed). It therefore implies a new, non-classical space-time structure [12,13].…”

Section: Modified Bracketsmentioning

confidence: 99%

“…Several independent studies have shown that holonomy and inverse-triad corrections from loop quantum gravity (LQG) modify hypersurface-deformation brackets for spherically symmetric gravity and related midisuperspace models [1][2][3][4][5][6][7][8][9][10], thereby realizing a deformation of general covariance [11][12][13]. These modifications are closely related [14] to anomalyfree models of perturbative cosmological inhomogeneity constructed within the same framework [15][16][17][18][19], suggesting that modified space-time structures may be a generic consequence of quantum-geometry effects in loop quantum gravity.…”

Section: Introductionmentioning

confidence: 99%

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Deformed covariance in spherically symmetric vacuum models of loop quantum gravity: Consistency in Euclidean and self-dual gravity

et al. 2020

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Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure of spacetime. Based on a canonical version of effective field theory, this paper provides a unified treatment, showing that modified space-time structures are generic in this setting. The special case of Euclidean gravity demonstrates agreement also with existing operator calculations.

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“…We do not always obtain new versions of space-time: generators can be redefined so as to absorb β [17], but only if this function does not change sign anywhere. If it does, for instance at large curvature in models of quantum gravity [18,19,20], a smooth transition from ǫ = −1 to ǫ = 1 in (4) implies a passage from Lorentzian space-time to Euclidean 4-space [21,22,23]. Such a model with non-singular signature change cannot be Riemannian.…”

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confidence: 99%

Symmetries of spacetime

Bojowald

2016

Int. J. Mod. Phys. D

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The equations of Hamiltonian gravity are often considered ugly cousins of the elegant and manifestly covariant versions found in the Lagrangian theory. However, both formulations are fundamental in their own rights because they make different statements about the nature of space-time and its symmetries. These implications, along with the history of their derivation and an introduction of recent mathematical support, are discussed here.General relativity is distinguished by its covariance under space-time diffeomorphisms, a large set of symmetries which guarantees coordinate independence and supplies fruitful links between physics and geometry. However, the symmetries are different in the Lagrangian and Hamiltonian pictures. Throughout an interesting history of work on Hamiltonian gravity, this under-appreciated state of affairs has led to pronouncements that verge on the heretical. Dirac, for instance -one of the outstanding protagonists -accompanied his detailed analysis in [1] by "It would be permissible to look upon the Hamiltonian form as the fundamental one, and there would then be no fundamental four-dimensional symmetry in the theory." He did not elaborate on this conclusion, but recent work in mathematics and physics provides an updated picture. If we put together contributions by relativists and mathematicians -some older and some recent -we can confirm the prescient nature of Dirac's insights. At the same time, we improve our fundamental understanding of space-time.The history of Hamiltonian gravity had begun well before Dirac's entry, spawned by questions about the analysis of the electromagnetic field. Starting in 1929, Heisenberg and Pauli [2,3] had applied canonical quantization to Maxwell's theory. An important issue was the covariance of their formulation, as it still is in the case of gravity. Rosenfeld [4] presented a detailed analysis of Hamiltonian general relativity, including a discussion of the important role of constraints. After a gap of almost 20 years, Bergmann and his collaborators turned the analysis of constraints into a program [5,6,7,8], in parallel with Dirac [9] not only in the timing of important work (1950) but also in apparent heresies: according to [5] "there is probably no particular reason why the theory of relativity must appear in the form of Riemannian geometry." The analysis of constraints most widely used today was developed by Dirac, and applied by him to gravity [1]. Dirac was able to bring Rosenfeld's results to a more convenient form by replacing general tetrads with * e-mail address: bojowald@gravity.psu.edu 1 metric variables adapted to a spatial foliation. The final step was made by Arnowitt, Deser and Misner in the 1960s [10], introducing a powerful parameterization of the space-time metric by lapse N, shift M a and the metric q ab on a spatial hypersurface. The resulting ADM formulation is widely used in numerical relativity, cosmology, and quantum gravity.An important question for Rosenfeld, following Heisenberg and Pauli, was the role of symmetries...

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Discreteness corrections and higher spatial derivatives in effective canonical quantum gravity

Cited by 38 publications

References 62 publications

Critical Evaluation of Common Claims in Loop Quantum Cosmology

Critical Evaluation of Common Claims in Loop Quantum Cosmology

Deformed covariance in spherically symmetric vacuum models of loop quantum gravity: Consistency in Euclidean and self-dual gravity

Symmetries of spacetime

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