Loop quantization of the Gowdy model with local rotational symmetry

Blas, Daniel Martín de; Olmedo, Javier; Pawłowski, Tomasz

doi:10.1103/physrevd.96.106016

Cited by 16 publications

(20 citation statements)

References 72 publications

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“…As argued by us throughout this paper, one needs to find an implementation of the 'improved dynamics' scheme in LQG and our algebraic results forms a first step towards this direction. The use of aμ-scheme can, perhaps, also ameliorate some of the problems arising in a model of (polarized) Gowdy cosmology, with an additional rotational symmetry, with regards to Dirac observables in the semi-classical limit [29,64].…”

Section: Discussionmentioning

confidence: 99%

“…On the contrary, the consequences of working within a µ 0 versus aμ scheme has been much less investigated in inhomogeneous models. Indeed, in most of the investigations dealing with the inhomogeneous spherically symmetric background [26,27], or Gowdy system [28,29], the holonomy corrections are implemented within the µ 0 -scheme prior to quantization. While the quantum theory can be constructed, it generates inconsistencies when solving the effective fields equations.…”

Section: Theμ Versus µ 0 -Scheme In Inhomogeneous Effective Modelsmentioning

confidence: 99%

“…This makes the quantum-corrected constraint ultra-local, which can lead to some problems in the infra-red (see, for instance,[29]. )…”

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confidence: 99%

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Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

Achour¹,

Brahma

2018

Phys. Rev. D

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When applying the techniques of Loop Quantum Gravity (LQG) to symmetry-reduced gravitational systems, one first regularizes the scalar constraint using holonomy corrections, prior to quantization. In inhomogeneous system, where a residual spatial diffeomorphism symmetry survives, such modification of the gauge generator generating time reparametrization can potentially lead to deformations or anomalies in the modified algebra of first class constraints. When working with self-dual variables, it has already been shown that, for spherically symmetric geometry coupled to a scalar field, the holonomy-modified constraints do not generate any modifications to general covariance, as one faces in the real variables formulation, and can thus accommodate local degrees of freedom in such inhomogeneous models. In this paper, we extend this result to Gowdy cosmologies in the self-dual Ashtekar formulation. Furthermore, we show that the introduction of aμ−scheme in midisuperspace models, as is required in the 'improved dynamics' of LQG, is possible in the self-dual formalism while being out of reach in the current effective models suing real-valued Ashtekar-Barbero variables.Our results indicate the advantages of using the self-dual variables to obtain a covariant loop regularization prior to quantization in inhomogeneous symmetry reduced polymer models, implementing additionally the crucialμ-scheme, and thus a consistent semiclassical limit. 2

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Section: Discussionmentioning

confidence: 99%

Section: Theμ Versus µ 0 -Scheme In Inhomogeneous Effective Modelsmentioning

confidence: 99%

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Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

Achour¹,

Brahma

2018

Phys. Rev. D

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“…Thus, the Schwarzschild solution, to compare the regularized solution with, reduces to 36) in the region where the curvature is high. We see that both α and γ −1 are regularized compared to the classical Schwarzschild solution as shown in Fig.…”

Section: Comparing With the Schwarzschild Solutionmentioning

confidence: 99%

Non-singular black holes and the limiting curvature mechanism: a Hamiltonian perspective

Achour

Lamy

Liu

et al. 2018

J. Cosmol. Astropart. Phys.

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We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian structure of the theory. We write down the equations of motion that we solve in the regime deep inside the black hole, and we recover that the black hole has no singularity, due to the limiting curvature mechanism. Then, we study the relation between such black holes and effective polymer black holes which have been introduced in the context of loop quantum gravity. As expected, contrary to what happens in the cosmological sector, mimetic gravity with a limiting curvature fails to reproduce the usual effective dynamics of spherically symmetric loop quantum gravity which are generically not covariant. Nonetheless, we exhibit a theory in the class of extended mimetic gravity whose dynamics reproduces the general shape of the effective corrections of spherically symmetric polymer models, but in an undeformed covariant manner. These covariant effective corrections are found to be always metric dependent, i.e. within theμscheme, underlying the importance of this ingredient for inhomogeneous polymer models. In that respect, extended mimetic gravity can be viewed as an effective covariant theory which naturally implements a covariant notion of point wise holonomy-like corrections. The difference between the mimetic and polymer Hamiltonian formulations provides us with a guide to understand the deformation of covariance in inhomogeneous polymer models.

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“…1. The so called Abelianization procedure [26] when applied to cosmological models (see in particular an application to Gowdy cosmology [27]) allows to bring the (otherwise unbearably complicated) evolution generator to the form quite similar to the one known from isotropic sector of LQC. Provided, that the method is improved to unambiguously reproduce general relativity as its low energy limit, that property in principle allows to apply the methods discussed in this article either directly or after an extension.…”

Section: Perspectivesmentioning

confidence: 99%

Universe’s memory and spontaneous coherence in loop quantum cosmology

Pawłowski

2016

Int. J. Mod. Phys. D

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The quantum bounce a priori connects several (semi)classical epochs of Universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of knowledge in that regards in the isotropic sector of loop quantum cosmology. This knowledge is next extended by studies of an isotropic universe admiting positive cosmological constant (featuring an infinite chain of large Universe epochs). It is also shown, that such universe always admits a semiclassical epoch thanks to spontaneous spontaneous coherence, provided it is semiclassical in certain constant of motion playing the role of energy.

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Loop quantization of the Gowdy model with local rotational symmetry

Cited by 16 publications

References 72 publications

Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

Non-singular black holes and the limiting curvature mechanism: a Hamiltonian perspective

Universe’s memory and spontaneous coherence in loop quantum cosmology

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