Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme

Alesci, Emanuele; Botta, Gioele; Stagno, Gabriele V.

doi:10.1103/physrevd.97.046011

Cited by 20 publications

(47 citation statements)

References 44 publications

(100 reference statements)

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“…II.4. Notice that the operators in (16) and (17) do not correspond geometrically to their classical equivalents, since the Ashtekar connection has dimension of a length −1 , while the eigenvalue of the densitized dreibein operator has dimension of ak × length, and thus length 3 . The proper rescaling has been suggested by LQC [3], and later adapted to QRLG extending Bianchi I metric to an inhomogeneous model [13].…”

Section: Ii3 Dewitt Coordinate Representationmentioning

confidence: 99%

“…along the link l 3 . Following Alesci and Cianfrani [13][14][15][16]18], we impose the DeWitt representation (17) -this is not completely rigorous (see Sec. IV-VI), but is sufficient for our purposes -gettinĝ…”

Section: Ii3 Dewitt Coordinate Representationmentioning

confidence: 99%

“…Quantum reduced loop gravity (QRLG) is chronologically one of the latest attempts, developed in [13][14][15][16] -for a review see [18]. It relies on imposing weak gauge-fixing conditions to the states of the kinematical Hilbert space of the full theory, LQG.…”

Section: Introductionmentioning

confidence: 99%

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Critical insight into the cosmological sector of loop quantum gravity

Bilski

Marcianò

2020

Phys. Rev. D

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This article sheds new light on the problem of cosmological reduction in Loop Quantum Gravity. We critically analyze Quantum Reduced Loop Gravity -an attempt to extract the cosmological sector of the full theory. We reconsider the reduction procedure applied to the states of the kinematical Hilbert space, developing a comparative analysis with previous efforts in the literature. We show that the constraints of the model were formerly instantiated in an inconsistent fashion, leading to an overconstrained dynamics and an ill-defined Hilbert space. We then scrutinize alternative implementations of symmetry-reduction. While remaining unaffected by the shortcomings encountered in Quantum Reduced Loop Gravity, these latter procedures bridge the gap between the full theory and former endeavors in Loop Quantum Cosmology. * bilski@zjut.edu.cn † marciano@fudan.edu.cn i The well known non-trivial structure of the vacuum was emphasized for gauge theories, providing a possible framework to account for quantum theories of gravity, by inspections of their instantonic solutions, as argued in Ref.[2].

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Section: Ii3 Dewitt Coordinate Representationmentioning

confidence: 99%

Section: Ii3 Dewitt Coordinate Representationmentioning

confidence: 99%

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Critical insight into the cosmological sector of loop quantum gravity

Bilski

Marcianò

2020

Phys. Rev. D

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“…A crucial ingredient for this procedure is the choice of weight for each graph. In the simpler cosmological setting [26], a somehow ad hoc combinatorial factor was chosen motivated by the statistical counting of microstates compatible with macroscopic configurations. In the black hole case, previous experience with entropy counting may lend important guidance for a physically better motivated choice.…”

Section: Discussion Of Resultsmentioning

confidence: 99%

Quantum gravity predictions for black hole interior geometry

2019

Self Cite

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In a previous work we derived an effective Hamiltonian constraint for the Schwarzschild geometry starting from the full loop quantum gravity Hamiltonian constraint and computing its expectation value on coherent states sharply peaked around a spherically symmetric geometry. We now use this effective Hamiltonian to study the interior region of a Schwarzschild black hole, where a homogeneous foliation is available. Descending from the full theory, our effective Hamiltonian, though still bearing the well known ambiguities of the quantum Hamiltonian operator, preserves all relevant information about the fundamental discreteness of quantum space. This allows us to have a uniform treatment for all quantum gravity holonomy corrections to spatially homogeneous geometries, unlike the minisuperspace loop quantization models in which the effective Hamiltonian is postulated. We show how, for several geometrically and physically well motivated choices of coherent states, the classical black hole singularity is replaced by a homogeneous expanding Universe. The resultant geometries have no significant deviations from the classical Schwarzschild geometry in the pre-bounce sub-Planckian curvature regime, evidencing the fact that large quantum effects are avoided in these models. In all cases, we find no evidence of a white hole horizon formation. However, various aspects of the post-bounce effective geometry depend on the choice of quantum states.A primary aim for the quantization program of gravitational field is to determine the fate of classical spacetime singularities as predicted by general relativity. It has been speculated that quantum gravitational effects smooth out spacetime singularities, analogously to how an ultraviolet completion of quantum fields tames ultraviolet divergences. Fortunately, the canonical approach to loop quantum gravity (LQG) is now sufficiently developed to systematically resolve this key issue from the full theory perspective.To provide some historical context, we point out that the first generation of quantum gravity predictions were made in cosmology and within the minisuperspace quantization scheme. There the loop quantization program was implemented by applying LQG inspired techniques to a (model dependent) symmetry reduced phase space of general relativity parametrized by the Ashtekar connection and densitized triad [1]. The resultant models, which later became known as loop quantum cosmology (LQC), unanimously predict that the classical spacetime singularity is replaced by a quantum bounce [2,3]. They offered the first glimpse of how quantum gravity could resolve spacetime singularities.However, attempts to generalize the loop quantization program to a black hole geometry were not equally successful at producing generally accepted predictions [4][5][6][7][8][9][10][11][12][13][14]. The starting point of all these previous attempts was the observation that the Schwarzschild black hole interior can be described in terms of a contracting anisotropic Kantowski-Sachs model, allowing one to apply ...

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“…A first step in this direction was taken in [97,98], where the homogeneity is based on conditions on the triads. The eigenvalues of the triads characterize the size of a fundamental cell and this can be seen as a discretization ambiguity, see also the discussion in [99,100]. An alternative framework is group field theory cosmology [101][102][103].…”

Section: √λmentioning

confidence: 99%

Cosmological Constant from Condensation of Defect Excitations

Dittrich

2018

Universe

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A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales. Here we define a family of (2 + 1)-dimensional quantum gravity states which arise from curvature excitations concentrated at point like defects and describe homogeneously curved geometries on large scales. These states represent therefore vacua for three-dimensional gravity with different values of the cosmological constant. They can be described by an anomaly-free first class constraint algebra quantized on one and the same Hilbert space for different values of the cosmological constant. A similar construction is possible in four dimensions, in this case the curvature is concentrated along string-like defects and the states are vacua of the Crane-Yetter model. We will sketch applications for quantum cosmology and condensed matter.

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Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme

Cited by 20 publications

References 44 publications

Critical insight into the cosmological sector of loop quantum gravity

Critical insight into the cosmological sector of loop quantum gravity

Quantum gravity predictions for black hole interior geometry

Cosmological Constant from Condensation of Defect Excitations

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