Quantum Cosmology

Kiefer, Claus; Sandhoefer, Barbara

doi:10.48550/arxiv.0804.0672

Cited by 21 publications

(31 citation statements)

References 33 publications

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“…The hope is that a consistent quantum theory of gravity is free of such singularities. This aspect can most easily be investigated in the framework of quantum cosmology: the application of quantum theory to the Universe as a whole [13,14]. Because of our restriction to homogeneous models, the corresponding framework of quantum cosmology does not encounter the mathematical problems of the full theory.…”

Section: Introductionmentioning

confidence: 99%

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Quantum fate of singularities in a dark-energy dominated universe

Bouhmadi-López¹,

Kiefer

Sandhöfer

et al. 2009

Phys. Rev. D

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Classical models for dark energy can exhibit a variety of singularities, many of which occur for scale factors much bigger than the Planck length. We address here the issue whether some of these singularities, the big freeze and the big démarrage, can be avoided in quantum cosmology. We use the framework of quantum geometrodynamics. We restrict our attention to a class of models whose matter content can be described by a generalized Chaplygin gas and be represented by a scalar field with an appropriate potential. Employing the DeWitt criterium that the wave function be zero at the classical singularity, we show that a class of solutions to the Wheeler-DeWitt equation fulfilling this condition can be found. These solutions thus avoid the classical singularity. We discuss the reasons for the remaining ambiguity in fixing the solution.

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Section: Introductionmentioning

confidence: 99%

“…Notice that the boundary condition imposed in[44,45] cannot be applied in our model with a phantom scalar field. The reason is that the scalar field is bounded in this case, so we cannot take the limit |φ| → ∞ in ϕ k (α, φ) 14. In taking this limit, notice that En(α) can become complex.…”

mentioning

confidence: 99%

Quantum fate of singularities in a dark-energy dominated universe

Bouhmadi-López¹,

Kiefer

Sandhöfer

et al. 2009

Phys. Rev. D

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“…[14,15,16] (for a recent review of the Wheeler-DeWitt equation in cosmology, see Ref. [17]). In particular, our starting point will be a modified Schrödinger equation for the quantum state of a mode of a minimally coupled scalar field in the de Sitter Universe as obtained within this approach in Ref.…”

Section: Introductionmentioning

confidence: 99%

Hints of (trans-Planckian) asymptotic freedom in semiclassical cosmology

Appignani

Casadio

2008

J. Cosmol. Astropart. Phys.

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We employ the semiclassical approximation to the Wheeler-DeWitt equation in the spatially flat de Sitter Universe to investigate the dynamics of a minimally coupled scalar field near the Planck scale. We find that, contrary to naïve intuition, the effects of quantum gravitational fluctuations become negligible and the scalar field states asymptotically approach plane-waves at very early times. These states can then be used as initial conditions for the quantum states of matter to show that each mode essentially originated in the minimum energy vacuum. Although the full quantum dynamics cannot be solved exactly for the case at hand, our results can be considered as supporting the general idea of asymptotic safety in quantum gravity.

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“…The detailed form of these terms can be found in [2,53,39]. Future investigations should deal with a concrete application of these terms in cosmology, for example, in the search for quantum gravitational effects in the anisotropy spectrum of the Cosmic Background Radiation.…”

Section: Quantum Gravitational Correctionsmentioning

confidence: 99%

“…In this subsection, I shall focus on some recent work into which I was myself involved. More detailed overviews of quantum cosmology can be found, for example, in [2,50,51,52,53].…”

Section: Quantum Cosmologymentioning

confidence: 99%

Quantum geometrodynamics: whence, whither?

Kiefer

2009

Gen Relativ Gravit

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Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler-DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.Keywords Quantum gravity · quantum cosmology · black holes PACS 04.60.-m · 04.60.Ds · 04.62.+v These considerations reveal that the concepts of spacetime and time itself are not primary but secondary ideas in the structure of physical theory. These concepts are valid in the classical approximation. However, they have neither meaning nor application under circumstances when quantum-geometrodynamical effects become important. . . . There is no spacetime, there is no time, there is no before, there is no after. The question what happens "next" is without meaning.

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Quantum Cosmology

Cited by 21 publications

References 33 publications

Quantum fate of singularities in a dark-energy dominated universe

Quantum fate of singularities in a dark-energy dominated universe

Hints of (trans-Planckian) asymptotic freedom in semiclassical cosmology

Quantum geometrodynamics: whence, whither?

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