Singularity-free and non-chaotic inhomogeneous Mixmaster in polymer representation for the volume of the universe

Antonini, Stefano; Montani, Giovanni

doi:10.1016/j.physletb.2019.01.050

Cited by 26 publications

(44 citation statements)

References 55 publications

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“…This surprising feature is predictably the consequence of the chosen isotropic variable, which in the standard Misner formulation corresponds to the logarithm of the natural Universe scale factor. Actually, discretizing the α Misner variable, we are discretizing the Universe volume, but without forbidding its zero value, like it is done in the case of a polymer discretization of the cubed scale factor, see [19,17].…”

Section: Discussionmentioning

confidence: 99%

Polymer representation of the Bianchi IX cosmology in the Misner variables

Giovannetti

Montani

2019

Phys. Rev. D

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We analyze the Bianchi IX Universe in the Polymer Quantum Mechanics framework, by facing both semiclassical and purely quantum effects near the cosmological singularity. The peculiar feature of the presented study is that we adopt Misner variables to describe the model dynamics, applying the polymer paradigm simultaneously to the isotropic one (linked to the Universe volume) and to the two anisotropy ones (characterizing the physical gravitational degrees of freedom). Setting two different cut-off scales for the two different variable sets, i.e. the geometrical volume and the gravity tensor modes, we demonstrate how the semiclassical properties of the Bianchi IX dynamics are sensitive to the ratio of the cut-off parameters. In particular, the semiclassical evolution turns out to be chaotic only if the parameter associated to the volume discretization is greater or equal to that one of the anisotropies. Then, we perform, for the chaotic case, a purely quantum polymer analysis, demonstrating that the original Misner result concerning the existence of quasi-classical states near the singularity (in the sense of high occupation numbers) is still valid in the revised approach and able to account for cut-off physics effects. The possibility for a comparison with the original study by Misner is possible because, for all the parameter space, the singularity is still present in the semiclassical evolution of the cosmological model. We interpret this surprising feature as the consequence of a geometrical volume discretization which does not prevent the volume to vanish, i.e. restoring in the Minisuperspace analysis the zero eigenvalue for the volume spectrum.

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Section: Discussionmentioning

confidence: 99%

Polymer representation of the Bianchi IX cosmology in the Misner variables

Giovannetti

Montani

2019

Phys. Rev. D

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“…where B = B(µ) is the eigeinvalue of the inverse volume operator appearing in the matter constraint (38):…”

Section: Dynamicsmentioning

confidence: 99%

“…The solution in the void case is the famous Kasner solution where a i (t) ∝ t k i , where k i are the constant Kasner indices that obey [112]; usually, these indices are parametrized through a variable u ∈ (1, +∞). Repeating the procedure of the isotropic sector, we introduce matter in the form of a scalar field φ obeying a Hamiltonian similar to (38) and playing the role of relational time; then, we quantize the system according to the Dirac procedure, following [79]. Now, when implementing theμ scheme, we are naturally induced to use three different parametersμ i relating to the three different directions.…”

Section: Bianchi Type Imentioning

confidence: 99%

“…Therefore, its employment in the cosmological sector has great relevance in trying to overcome the singularity issue of GR and making also a comparison with the LQC main results regarding the presence of an initial Big Bounce and its properties. In this sense, the principal feature of the polymer approach is making clear that the properties of the cosmological dynamics are strongly dependent on the set of variables on which the polymer quantization is implemented [27,34,38,42,44,45].…”

Section: Polymer Cosmologymentioning

confidence: 99%

“…We will also provide an interesting comparison of the cosmological implementation of the PQM in the metric representation. In particular, we will compare the analyses in [34,38,42], where the homogeneous and inhomogeneous Mixmaster dynamics is studied through the polymerization of the standard Misner isotropic variable α and of the Universe volume, respectively: the difference is only in using or not using a logarithm in the definition of the isotropic variable, but the implication is very deep since only the volume representation ensures a bouncing cosmology. Furthermore, questions concerning the chaotic or non-chaotic nature of the semiclassical Bianchi IX dynamics are addressed in some detail.…”

Section: Introductionmentioning

confidence: 99%

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An Overview on the Nature of the Bounce in LQC and PQM

2021

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We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, when a pure metric approach is concerned, showing how, in general, the primordial singularity is not removed by the quantum effects. We then analyze the main implications of applying the loop quantum gravity prescriptions to the minisuperspace model, i.e., we discuss the basic features of the so-called loop quantum cosmology. For the isotropic Universe dynamics, we compare the original approach, dubbed the μ0 scheme, and the most commonly accepted formulation for which the area gap is taken as physically scaled, i.e., the so-called μ¯ scheme. Furthermore, some fundamental results concerning the Bianchi Universes are discussed, especially with respect to the morphology of the Bianchi IX model. Finally, we consider some relevant criticisms developed over the last ten years about the real link existing between the full theory of loop quantum gravity and its minisuperspace implementation, especially with respect to the preservation of the internal SU(2) symmetry. In the second part of the review, we consider the dynamics of the isotropic Universe and of the Bianchi models in the framework of polymer quantum mechanics. Throughout the paper, we focus on the effective semiclassical dynamics and study the full quantum theory only in some cases, such as the FLRW model and the Bianchi I model in the Ashtekar variables. We first address the polymerization in terms of the Ashtekar–Barbero–Immirzi connection and show how the resulting dynamics is isomorphic to the μ0 scheme of loop quantum cosmology with a critical energy density of the Universe that depends on the initial conditions of the dynamics. The following step is to analyze the polymerization of volume-like variables, both for the isotropic and Bianchi I models, and we see that if the Universe volume (the cubed scale factor) is one of the configurational variables, then the resulting dynamics is isomorphic to that one emerging in loop quantum cosmology for the μ¯ scheme, with the critical energy density value being fixed only by fundamental constants and the Immirzi parameter. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model by means of a metric approach. In particular, we compare the results obtained by using the volume variable, which leads to the emergence of a singularity- and chaos-free cosmology, to the use of the standard Misner variable. In the latter case, we deal with the surprising result of a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations of the problem of changing variables in the polymer representation of the minisuperspace dynamics. In particular, on a semiclassical level, we consider how the dynamics can be properly mapped in two different sets of variables (at the price of having to deal with a coordinate dependent lattice step), and we infer some possible implications on the equivalence of the μ0 and μ¯ scheme of loop quantum cosmology.

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