Classical and quantum behavior of the generic cosmological solution

Imponente, Giovanni; Montani, Giovanni

doi:10.1063/1.2399600

Cited by 9 publications

(11 citation statements)

References 11 publications

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“…Such a logarithmic behavior confirms, also in the polymer framework, the estimate provided in [53]. It is well-known [44] that, in the standard picture and in the limit V → 0, the terms exp(β a + β b ) with a = b are negligible with respect to exp(2β a ) where the potential is relevant. Thus, in the polymer framework, they are negligible if the condition V ≪ 1 is satisfied.…”

Section: Spatial Gradientssupporting

confidence: 84%

“…Following [44], we assume the Kasner vectors l a α to depend only on spatial coordinates. It is important to remark that this picture is not the most general.…”

Section: Inhomogeneous Mixmastermentioning

confidence: 99%

“…is the inhomogeneous generalization of the potential of the Bianchi models. The last term in equation ( 4) can be neglected in the limit V → 0 [44]. Unlike the homogeneous case, the quantities λ a are not constant, but they are defined as…”

Section: Inhomogeneous Mixmastermentioning

confidence: 99%

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

Antonini

Montani

2019

Physics Letters B

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We analyze the semiclassical polymer dynamics of the inhomogeneous Mixmaster model by choosing the cubed scale factor as the discretized configurational variable, while the anisotropies remain pure Einsteinian variables. Such a modified theory of gravity should be regarded as the appropriate framework to describe the behavior of quantum mean values, both in polymer quantum mechanics and in Loop Quantum Cosmology. We first construct the generalized Kasner solution, including a massless scalar field and a cosmological constant in the dynamics. They account for a quasi-isotropization, inflationary-like mechanism. The resulting scenario links a singularity-free Kasner-like regime with a homogeneous and isotropic de Sitter phase. Subsequently, we investigate the role of the three-dimensional scalar curvature, demonstrating that a bounce of the point-universe against the potential walls can always occur within the polymer framework, also in the presence of a scalar field. However, the absence of the singularity implies that the curvature is bounded. Therefore, the point-universe undergoes an oscillatory regime until it oversteps the potential walls (if the Big Bounce is not reached before). After that, a final stable Kasner-like regime will last until the Big Bounce. Thus, the present study demonstrates that, as soon as a discretization of the volume of the universe is performed, the generic cosmological solution is non-chaotic and free from singularities. It is likely that the same result can be achieved also in the loop quantum cosmology approach.

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Section: Spatial Gradientssupporting

confidence: 84%

“…Following [44], we assume the Kasner vectors l a α to depend only on spatial coordinates. It is important to remark that this picture is not the most general.…”

Section: Inhomogeneous Mixmastermentioning

confidence: 99%

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

Antonini

Montani

2019

Physics Letters B

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“…The first attempt to implement the canonical quantum gravity approach developed in [1][2][3] to the cosmological setting was due to the analysis proposed in [54], where the Bianchi IX Universe was studied within certain approximations, and the most relevant properties of its quantum dynamics were elucidated (for extensions of this approach to generic inhomogeneous models, see [55][56][57][58][59][60][61][62], and for a refined numerical study of the Bianchi IX quantization, see [63]).…”

Section: Cosmological Quantum Dynamicsmentioning

confidence: 99%

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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“…The quantum dynamics of the Bianchi type IX geometry in the vicinity of the singularity was examined by Misner [2] back in 1969; later on, it was examined by other authors (for example, see [3] or [4]) who complemented and expanded his approach.…”

Section: Introductionmentioning

confidence: 98%

Effective gravitational equations induced by quantum effects of a scalar field in the Bianchi type IX spaces

Кириллова

2008

Russ Phys J

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530.12The effective gravitational equations induced by quantum effects of a scalar field in the Bianchi type IX spacetime are derived in the present work. The curvature tensor components and their combinations are calculated in the Bianchi type IX spaces. To estimate a one-loop effective action, the asymptotic Schwinger-DeWitt perturbative formula with consideration of terms up to the second order is used. Quantum corrections involve the fourth-order derivative of the metric; as a consequence, the background gravitational action also includes terms up to the fourth-order derivatives of the metric.

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Classical and quantum behavior of the generic cosmological solution

Cited by 9 publications

References 11 publications

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

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

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

Effective gravitational equations induced by quantum effects of a scalar field in the Bianchi type IX spaces

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