Semiclassical and quantum analysis of the isotropic Universe in the polymer paradigm

Montani, Giovanni; Mantero, Claudia; Bombacigno, Flavio; Cianfrani, Francesco; Barca, Gabriele

doi:10.1103/physrevd.99.063534

Cited by 23 publications

(39 citation statements)

References 57 publications

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“…Furthermore, the Big Bounce has also the features of a universal cut-off since the critical energy density of the Universe takes a maximum value depending only on fundamental constants and the Immirzi parameter. This result is obtained in the improved scheme of LQC as shown in Section 3.3 and also demonstrated in the context of PQM for the isotropic model in [37]. Moreover, similar results to those obtained in theμ scheme are outlined in [44,45] when PQM is implemented on volume-like variables.…”

Section: Discussionsupporting

confidence: 77%

“…In particular, when the Universe volume itself is considered to be one of the configurational variables, it is possible to derive a polymer modified Friedmann equation for the Bianchi I model. We will see that the total critical energy density has universal features, as demonstrated in [37] for the isotropic case.…”

Section: Polymer Cosmology In the Volume-like Variablesmentioning

confidence: 55%

“…For instance, it is necessary to better characterize the physical properties of the Big Bounce, both by providing a pure quantum description instead of just a semiclassical one, and by further investigating the thermodynamical nature of the quantum cosmological fluid. Moreover, it is crucial to understand how a collapsing Universe before our expanding branch is generated and how it can influence the morphology of the present Universe (see some pioneering works [37,39,[132][133][134][135][136][137][138]). A typical example of this issue affecting bouncing cosmologies is provided in [37], where it is argued that the flatness paradox is still present, even though the horizon paradox is naturally solved, thanks to the pre-existing collapsing Universe.…”

Section: Discussionmentioning

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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Section: Discussionsupporting

confidence: 77%

Section: Polymer Cosmology In the Volume-like Variablesmentioning

confidence: 55%

Section: Discussionmentioning

confidence: 99%

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

2021

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“…where ρ T OT takes into account the fluid's presence. In order to derive the latter, the canonical transformation a 3 → V has been performed; one chooses the volume V as the preferred Polymer variable because with this choice the critical density ρ c will be scale factor independent [18]. The Polymer approximation will then change the Friedmann equatioñ…”

Section: Semi-classical Polymer Dynamicsmentioning

confidence: 99%

“…In order to remove the obtained singularity in the considered cosmological model we introduce a notion of cutoff physics in the Minisuperspace via the Polymer quantum mechanics approach [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Specific entropy as a clock for the evolutionary quantization of the isotropic Universe

Campolongo

Montani

2020

Eur. Phys. J. C

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In this paper, we analyze the dynamics of an isotropic closed Universe in presence of a cosmological constant term and we compare its behavior in the standard Wheeler–DeWitt equation approach with the one when a Lagrangian fluid is considered in the spirit of the Kuchar–Brown paradigm. In particular, we compare the tunnelling of the Universe from the classically forbidden region to the allowed one, showing that considering a time evolution deeply influences the nature of the model. In fact, we show that in the presence of the Lagrangian fluid, the cosmological singularity is restored both in the classical and the quantum regime. However, in the quantum regime the singularity is probabilistically suppressed for some energy eigenvalues and in the case the latter is equal to zero one recovers the standard WDW case. Finally, we introduce a cut-off physics feature in the Minisuperspace by considering a Polymer quantum mechanical approach limiting our attention to the semi-classical dynamics mainly (the quantum treatment is inhibited by the non-local nature of the Hamiltonian operator). We show that the singularity is again removed, like in the fluid-free model, and a bouncing cosmology emerges so that the present model could mimic a cyclic cosmology.

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