Quantum Cosmology - The Supersymmetric Perspective - Vol. 1

Moniz, Paulo Vargas

doi:10.1007/978-3-642-11575-2

Cited by 60 publications

(78 citation statements)

References 8 publications

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“…We suppose that the recent study of the Hamiltonian analysis of gravity [45] may give a certain direction in the investigation of quantum cosmology for this reason. We consider that supersymmetric quantum cosmology [46], which deals with an extended constraint system, may be an interesting target to study about reduction of phase space.…”

Section: Discussionmentioning

confidence: 99%

Equivalent Hamiltonian approach to quantum cosmology of integrable models

Kan

Kuniyasu

Shiraishi

et al. 2020

Class. Quantum Grav.

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Section: Discussionmentioning

confidence: 99%

Equivalent Hamiltonian approach to quantum cosmology of integrable models

Kan

Kuniyasu

Shiraishi

et al. 2020

Class. Quantum Grav.

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“…where V 0 is given by We observe that for a matter-dominated case, our model yields two disconnected branches. 8 However, for both of the branches, by assuming a 3 0 ψ 0 > 0, the time behavior of the scalar field depends not only on the sign of the c 1 β but also on the signs of c 1 and β. We have shown that for different values of n, dependent on the signs of c 1 and β, the scalar field can whether contracts or expands with the cosmic time.…”

Section: (Effective) Dust Cosmologiesmentioning

confidence: 99%

“…Higher-dimensional models of the universe have been widely studied: Kaluza-Klein (KK) theories [4][5][6], tendimensional and eleven-dimensional supergravity [7][8][9] as well as string theories [10,11]. In particular, Kaluza considered a five-dimensional space-time, under the following key assumptions [6], to bring together electromagnetism with general relativity (GR): (i) there is no ordinary matter in the higher dimensional space-time, (ii) geometrical quantities similar to those defined in GR were introduced and (iii) the cylinder condition for the extra coordinate was assumed, which implies that the derivatives with respect to the extra dimension must vanish.…”

Section: Introductionmentioning

confidence: 99%

Modified Saez–Ballester scalar–tensor theory from 5D space-time

Rasouli

Moniz

2017

Class. Quantum Grav.

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In this paper, we bring together the five-dimensional Saez-Ballester (SB) scalar-tensor theory [1] and the induced-matter-theory (IMT) setting [2], to obtain a modified SB theory (MSBT) in four dimensions. Specifically, by using an intrinsic dimensional reduction procedure into the SB field equations in five-dimensions, a MSBT is obtained onto a hypersurface orthogonal to the extra dimension. This four-dimensional MSBT is shown to bear distinctive new features in contrast to the usual corresponding SB theory as well as to IMT and the Modified Brans-Dicke Theory (MBDT) [3]. In more detail, besides usual induced matter terms retrieved through the IMT, the MSBT scalar field is provided with additional physically distinct (namely, SB induced) terms as well as an intrinsic self-interacting potential (interpreted as consequence of the IMT process and the concrete geometry associated to the extra dimension). Moreover, our MSBT has four sets of field equations, with two sets having no analog in the standard SB scalar-tensor theory. It should be emphasized that the herein appealing solutions can emerge solely from the geometrical reductional process, from presence also of extra dimension(s) and not from any ad-hoc matter either in the bulk or on the hypersurface. Subsequently, we apply the herein MSBT to cosmology and consider an extended spatially flat FLRW geometry in a five-dimensional vacuum space-time. After obtaining the exact solutions in the bulk, we proceed to construct, by means of the MSBT setting, the corresponding dynamic, on the four-dimensional hypersurface. More precisely, we obtain the (SB) components of the induced matter, including the induced scalar potential terms. We retrieve two different classes of solutions. Concerning the first class, we show that the MSBT yields a barotropic equation of state for the induced perfect fluid. We then investigate vacuum, dust, radiation, stiff fluid and false vacuum cosmologies for this scenario and contrast the results with those obtained in the standard SB theory, IMT and BD theory. Regarding the second class solutions, we show that the scale factor behaves similar to a de Sitter (DeS) model. However, in our MSBT setting, this behavior is assisted by non-vanishing induced matter instead, without any a priori cosmological constat. Moreover, for all these solutions, we show that the extra dimension contracts with the cosmic time.

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“…and the associated Levi-Civita connection. An important difference between our approach and numerous previous ones (see for instance Refs [ [14] - [20]]) is that we fix from the beginning the Lorentz gauge by univocally specifying a vierbein expressed as (time dependent) combinations of the 1-form dt and the three invariant forms on SU (2) : τ a (x) (which satisfy dτ a + ǫ a b c τ b ∧ τ c = 0). In terms of them the metric reads :…”

Section: The Minisuperspace Modelmentioning

confidence: 99%

Minisuperspace quantum supersymmetric cosmology (and its hidden hyperbolic Kac-Moody structures)

Damour

Spindel²

2017

The Fourteenth Marcel Grossmann Meeting

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This work summarises recent progress 1,2 obtained by the mini-superpspace quantization of N = 1, d = 4 supergravity, formulated in the framework of the Bianchi IX cosmological model. The emphasis is put on three main results: the completeness of the solution space obtained, the elements suggesting a hidden Kac-Moody structure of the theory and those leading to conjecture an avoidance of the cosmological singularity by some branches of the wave function of the Universe.Keywords: Quantum cosmology; supergravity; quantum gravity; Kac-Moody algebras. Some MotivationsIn the framework of Einstein gravity, under very general assumptions, several theorems 3 predict ineluctable occurrence of cosmological singularities. These singularities reflect the inadequacy of a classical description of the physics of the first instants of the Universe. The relevant theory -maybe a workable string field theory -is not yet known. However, we may think that the era since which physics is reasonably well described by a metric governed by general relativity is preceded by an epoch where a quantized version of it is relevant. Of course this is only a pis aller, comparable to the quantization of the hydrogen atom or to the Fermi model that can be seen as approximations to quantum electrodynamics or quantum non-abelian gauge theories.On the other hand, a study of classical cosmological solutions in the vicinity of their singularities 4,5 has shown that in a generic case the dynamics of the system becomes chaotic. Even homogeneous cosmologies like the Bianchi VIII or IX models approximately evolve as a succession of periods described by Kasner like metrics:separated by collisions. Here {θ k } is a set of SO(2, 1) or SU (2) invariant forms and {p k } the set of so-called Kasner exponents. These exponents are constants during each period, but randomly reshuffled by the collision processes. The evolution of the classical geometry of a general non-homogeneous model appears as an ensemble

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Quantum Cosmology - The Supersymmetric Perspective - Vol. 1

Cited by 60 publications

References 8 publications

Equivalent Hamiltonian approach to quantum cosmology of integrable models

Equivalent Hamiltonian approach to quantum cosmology of integrable models

Modified Saez–Ballester scalar–tensor theory from 5D space-time

Minisuperspace quantum supersymmetric cosmology (and its hidden hyperbolic Kac-Moody structures)

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