Anisotropic spinfoam cosmology

Rennert, Julian; Sloan, David

doi:10.1088/0264-9381/31/1/015017

Cited by 9 publications

(12 citation statements)

References 80 publications

(207 reference statements)

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“…The Daisy graph is perfectly suited to the relaxation of the restriction to isotropic models just by using three different holomorphic labels z i at each link. This will be our setting in the following paper [47]. Furthermore, we showed how one can reproduce the missing curvature term in the curved model, described by the Dipole graph, without using higher terms in the spin expansion.…”

Section: Discussionmentioning

confidence: 85%

“…Note further, that the identification with cosmology also arises because of the particular holonomies and fluxes which we are using: In this sense we identify our simple graph with a cosmological setting. The original motivation for this graph, especially the use of three closed links, was its potential applicability to anisotropic cosmological settings and therewith a physically more complex situation, a problem we will tackle in a follow up paper [47]. In this paper we will restrict our attention mostly to the isotropic case and see that this one node graph is already sufficient to reproduce the original result of [1].…”

Section: Our Modelmentioning

confidence: 99%

“…However, for the moment we go along with this strategy mainly for its computability but also for the following reasons: First, in [15] it was shown that using the factorizing amplitude it is possible to reproduce the de Sitter solution, which is a non-static universe. Second, in the follow up paper to this one [47] we will derive a anisotropic Bianchi I universe, which too possesses classicaly only dynamical solutions, using the factorizing amplitude. Thus, we leave the examination of non-factorizing transition amplitudes for future research.…”

Section: )mentioning

confidence: 99%

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A homogeneous model of spinfoam cosmology

Rennert¹,

Sloan²

2013

Class. Quantum Grav.

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We examine spinfoam cosmology by use of a simple graph adapted to homogeneous cosmological models. We calculate dynamics in the isotropic limit, and provide the framework for the anisotropic case. We calculate the transition amplitude between holomorphic coherent states on a single node graph and find that the resultant dynamics is peaked on solutions which have no support on the zero volume state, indicating that big bang type singularities are avoided within such models.

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Section: Discussionmentioning

confidence: 85%

Section: Our Modelmentioning

confidence: 99%

Section: )mentioning

confidence: 99%

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A homogeneous model of spinfoam cosmology

Rennert¹,

Sloan²

2013

Class. Quantum Grav.

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“…Less is known at the dynamical level. A number of approaches have been developed to address this problem, including spin foam cosmology [128][129][130][131][132] and quantumreduced loop gravity, whether based on one node representing all of space [133,134] or many nodes in a lattice [135][136][137][138][139]. The quantum Friedmann dynamics can be extracted in these approaches and the correct classical limit is recovered if an important lesson from LQC is used: the length of the holonomies constituting the field strength operator in the Hamiltonian constraint must depend on the densitized triad operator, as discussed in Sec.…”

Section: A Relation To Loop Quantum Gravitymentioning

confidence: 99%

Testing loop quantum cosmology

Wilson-Ewing

2017

Comptes Rendus. Physique

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Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the tensor-to-scalar ratio in the matter bounce scenario; these two effects are potential observational tests for loop quantum cosmology. In this article, I review these predictions and others, and also briefly discuss three open problems in loop quantum cosmology: its relation to loop quantum gravity, the trans-Planckian problem, and a possible transition from a Lorentzian to a Euclidean space-time around the bounce point.

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“…This choice has also been considered in[36] in the canonical context, and in[37,38] in the cosmological setting. The hypercubic lattice has also been investigated in the loop quantum gravity path integral framework in[39,40].…”

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confidence: 99%

Investigation of the spinfoam path integral with quantum cuboid intertwiners

2016

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In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the Spin Foam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov (EPRL-FK). To tackle the problem, we restrict to a set of quantum geometries that reflects the large amount of lattice symmetries. In particular, the sum over intertwiners is restricted to quantum cuboids, i.e. coherent intertwiners which describe a cuboidal geometry in the large-j limit.Using asymptotic expressions for the vertex amplitude, we find several interesting properties of the state sum. First of all, the value of coupling constants in the amplitude functions determines whether geometric or non-geometric configurations dominate the path integral. Secondly, there is a critical value of the coupling constant α, which separates two phases. In both phases, the diffeomorphism symmetry appears to be broken. In one, the dominant contribution comes from highly irregular, in the other from highly regular configurations, both describing flat Euclidean space with small quantum fluctuations around them, viewed in different coordinate systems. On the critical point diffeomorphism symmetry is nearly restored, however.Thirdly, we use the state sum to compute the physical norm of kinematical states, i.e. their norm in the physical Hilbert space. We find that states which describe boundary geometry with high torsion have exponentially suppressed physical norm. We argue that this allows one to exclude them from the state sum in calculations. I. MOTIVATIONThe spin foam approach has been developed to give a rigorous meaning to the path integral for quantum gravity (see [1] for a review). Its central idea rests on the observation that the first order formalism of GR can be rewritten as a certain constrained topological theory [2,3], dubbed "BF theory". A quantization choice for these constraints is what specifies the spin foam model, and in recent years there have been several proposals [4][5][6][7]. A popular choice has emerged in the so-called EPRL-FK model [5,8,9], which possesses quite useful properties. In particular, the resulting amplitude has an asymptotic expression for large quantum numbers which reproduces the Regge action [10][11][12]. Furthermore, the resulting path integral for the EPRL-FK model naturally has boundary states which resemble the spin network states from canonical loop quantum gravity [13][14][15], which is why it has been coined "covariant loop quantum gravity" ([16], see also [17,18]).There are several open questions, however. While there are numerous results available which elucidate the property of a single vertex amplitude, very little is known about the behaviour of the whole path integral.1 In particular, it is the realm of many building blocks which is of utmost importance if one wants to understand the * benjamin.bahr@desy.de † sebastian.steinhaus@desy.de 1 There are some results on the asymptotic expression for more than one vertex [19,20], as well as self-energy calculations [21].continuum limi...

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Anisotropic spinfoam cosmology

Cited by 9 publications

References 80 publications

A homogeneous model of spinfoam cosmology

A homogeneous model of spinfoam cosmology

Testing loop quantum cosmology

Investigation of the spinfoam path integral with quantum cuboid intertwiners

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