Expansions in spin foam cosmology

Hellmann, Frank

doi:10.1103/physrevd.84.103516

Cited by 19 publications

(28 citation statements)

References 36 publications

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“…This strategy amounts to the straightforward computation of spin foam transition amplitudes for boundary states that admit an interpretation in terms of homogeneous universes, and their re-writing in terms of an effective Hamiltonian constraint equation to be compared with the one of homogeneous GR. Beside technical aspects (see for example [49] for a critical analysis), the main differences stem from a change in perspective. While in GFT condensate cosmology one tries to extract an effective hydrodynamic description for the collective observables describing a large number of microscopic spin network degrees of freedom, here the focus is on the spin network degrees of freedom themselves and their fundamental quantum dynamics.…”

Section: Discussion: Answers To Frequently Asked Questions and Relmentioning

confidence: 99%

The universe as a quantum gravity condensate

Oriti

2017

Comptes Rendus. Physique

120

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This is an introduction to the approach to the extraction of cosmological dynamics from full quantum gravity based on group field theory condensates. We outline its general perspective, which sees cosmology as the hydrodynamics of the fundamental quantum gravity degrees of freedom, as well as its concrete implementation within the group field theory formalism. We summarise recent work showing the emergence of a bouncing cosmological dynamics from a fundamental group field theory model, and provide a brief but complete survey of other results in the literature. Finally, we discuss open issues and directions for further research.

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Section: Discussion: Answers To Frequently Asked Questions and Relmentioning

confidence: 99%

The universe as a quantum gravity condensate

Oriti

2017

Comptes Rendus. Physique

120

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“…Very coarse states would correspond to homogeneous configurations, finer states would describe inhomogeneities. Indeed, in the context of loop quantum cosmology [52], there are different suggestions on how the kinematics and dynamics can be obtained from the full theory [35,53,54] and how to include corrections from inhomogeneities, with Hellmann [54] discussing the (cylindrical) consistency conditions for the truncation of a given theory to homogeneous degrees of freedom.…”

Section: Summary Open Issues and Outlookmentioning

confidence: 99%

From the discrete to the continuous: towards a cylindrically consistent dynamics

Dittrich

2012

New J. Phys.

162

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Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations exactly mirror the continuum limit. As a standard tool for the kinematics of loop quantum gravity, we propose a coarse-graining procedure that aims at constructing a cylindrically consistent dynamics in the form of transition amplitudes and Hamilton's principal functions. The coarse-graining procedure, which is motivated by tensor network renormalization methods, provides a systematic approximation scheme for this purpose. A crucial role in this coarsegraining scheme is played by the embedding maps that allow interpretation of discrete boundary data as continuum configurations. These embedding maps should be selected according to the dynamics of the system, as the choice of embedding maps will determine the truncation of the renormalization flow. IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 4. Larger coarse-graining steps 10 5. Other coarse-graining schemes 13 6. Cylindrical consistency 15 7. Remarks on the quantum theory case 17 8. Summary, open issues and outlook 21 Acknowledgments 24 References 24 IntroductionDiscretizations have become a leading tool for the construction of quantum gravity models [1], for instance in loop quantum gravity [2, 3], spin foams [4,5] or Regge gravity [6]. Indeed, discrete models provide a very effective method for accessing non-perturbative physics. Given a discretization, the question arises as to how to relate observables from the discrete model to observables in the corresponding continuum limit (should it exist). Usually, this question is handled by considering a family of discretizations in which we can consider the refinement limit. Observables computed from given discretizations will, in general, be approximations to the corresponding observables in the continuum limit.An alternative view is provided by the concept of cylindrical consistency, which is a key technique in the construction of the continuum Hilbert space of loop quantum gravity [7]. The idea here is that discretizations are not seen as an approximation but as a selection of a certain set of degrees of freedom, for which the discrete model should give the same predictions as the continuum model. More precisely, discretizations come with a (partial) ordering into finer and coarser and embedding maps 1 of coarser into finer discretizations. Cylindrical consistency demands that observables that can be represented in a given discretization should not depend on the choice of finer discretization into which this given discretization is embedded. In other words, a prediction drawn from a given discretization should be also valid for any refined discretization or the continuum limit.So far this concept has been successfully applied to the construction of the kinematical Hilbert space of loop quantum gravity [2,7], including observables and the Hamiltonian constraints [8]. The question arises as to whether we can implement this concept for the dynamics, for instance in...

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“…Based on these results the asymptotic behaviour of several observables attached to a single weight was obtained in the BC model [44][45][46][47], as well as in the new models [48,49]. It is, however, unlikely that these type of calculations truly give information on any kind of general relativity limit, see for example the discussion in [50][51][52][53]. The behaviour of the entire state sum has remained largely unstudied, the exception being the results of [54], which indicate that some of the desirable geometric properties are lost once the entire state sum is considered, in particular the geometries that occur semi-classically are flat.…”

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confidence: 92%

Holonomy spin foam models: asymptotic geometry of the partition function

Hellmann

Kamiński

2013

J. High Energ. Phys.

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Abstract:We study the asymptotic geometry of the spin foam partition function for a large class of models, including the models of Barrett and Crane, Engle, Pereira, Rovelli and Livine, and, Freidel and Krasnov.The asymptotics is taken with respect to the boundary spins only, no assumption of large spins is made in the interior. We give a sufficient criterion for the existence of the partition function. We find that geometric boundary data is suppressed unless its interior continuation satisfies certain accidental curvature constraints. This means in particular that most Regge manifolds are suppressed in the asymptotic regime. We discuss this explicitly for the case of the configurations arising in the 3-3 Pachner move.We identify the origin of these accidental curvature constraints as an incorrect twisting of the face amplitude upon introduction of the Immirzi parameter and propose a way to resolve this problem, albeit at the price of losing the connection to the SU(2) boundary Hilbert space.The key methodological innovation that enables these results is the introduction of the notion of wave front sets, and the adaptation of tools for their study from micro local analysis to the case of spin foam partition functions.

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Expansions in spin foam cosmology

Cited by 19 publications

References 36 publications

The universe as a quantum gravity condensate

The universe as a quantum gravity condensate

From the discrete to the continuous: towards a cylindrically consistent dynamics

Holonomy spin foam models: asymptotic geometry of the partition function

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