Quantum cosmology: how to interpret and obtain results

Pinto-Neto, Nelson

doi:10.1590/s0103-97332000000200014

Cited by 8 publications

(18 citation statements)

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“…In summary, we can say that the general structure of the Bohmian approach to the quantum cosmology of (1) indeed stills valid for the class of orderings (27), in agreement with the argument of Ref. [23], but the description of the expansion of the universe itself, for given initial conditions α(t = 0), φ(t = 0), changes. More precisely, the modified Hamilton-Jacobi structure of Eq.…”

Section: Discussionsupporting

confidence: 85%

“…(20) for each coordinate, taking into account the sign of f i in order to avoid imaginary variables in Eq. (23). Finally, observe that, introducing the ordering parameter r ≥ 0, both (26) and the trivial ordering become particular cases of…”

Section: The Ordering Problemmentioning

confidence: 95%

“…In Ref. [23], it is shown that the basic features of Bohmian quantum gravity do not really depend on the factor ordering, although some ordering must be chosen to actually apply quantisation. Basead on that argument, it is common to apply only the trivial ordering in the quantization of the constrained Hamiltonian, like it is done in Ref.…”

mentioning

confidence: 99%

“…Basead on that argument, it is common to apply only the trivial ordering in the quantization of the constrained Hamiltonian, like it is done in Ref. [23]. But the factor ordering ambiguity remains, so that we can ask ourselves: if the general features of that theory are invariant under a change of ordering, what happens with the time evolution of the scale factor for a non-trivial ordering?An interesting non-trivial ordering was proposed by T. Christodoulakis and J. Zanelli in Refs.…”

mentioning

confidence: 99%

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Bouncing and cyclic quantum primordial universes and the ordering problem

Torres¹,

Fabris²,

Piattella³

2020

Class. Quantum Grav.

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In a Bohmian quantum cosmology scenario, we investigate some quantum effects on the evolution of the primordial universe arising from the adoption of an alternative non-trivial ordering to the quantization of the constrained Hamiltonian of a minimally coupled scalar field. The Wheeler-DeWitt equation has a contribution from the change in factor ordering, hence there are new quantum effects. We compare the results between the non-trivial and the trivial ordering cases, showing that the classical limit is valid for both orderings, but new bouncing and cyclic solutions are present in the non-trivial case. Additionally, we show that the non-singular solutions already present in the trivial ordering formalism keep valid. * Bohmian) quantum cosmology. In Refs. [7-9], it is described how such an alternative interpretation can be generalized from quantum mechanics to cosmological models such as those of Eq. (1). In particular, even when V = 0 one is able to solve the singularity problem thanks to quantum corrections, which induce a bounce. The case of an exponential potential, related with a matter-dominated universe, was recently presented in Ref. [10].The Lagrangian (1) can also be seen as one of the simplest particular cases of Horndeski modified gravity theory [11], thus it is free of Ostrogradsky instability [12,13]. It is also in agreement with the recent constraints imposed by GW170817 and GRB170817A [14-16] on the velocity of gravitational waves. See e.g. Ref.[13]. Lagrangian (1) is also related with effective string theory [7] and is also the Einstein frame version of several other scalar-tensor theories of gravity [5].The motivation for adopting an alternative interpretation of quantum mechanics in a cosmological setting comes from the fact that the exterior domain hypothesis [17], tacitly present in most standard interpretations of quantum mechanics, is considered by some authors as being a conceptual problem when the system under investigation is the universe [18][19][20]. Because of that, it has been proposed [20-23] to adopt in cosmology the Bohmian interpretation of quantum mechanics [24,25]. Besides that, the Bohmian interpretation also solves the problem of time ambiguity in quantum cosmology and quantum gravity [26,27], thanks to the guidance equations. More about Bohm-de Broglie quantum mechanics can be found in Refs. [28][29][30][31][32][33].Another conceptual problem faced in the quantisation of a gravitational theory like (1) is the factor ordering ambiguity, a direct consequence of Dirac's quantisation rule. In Ref. [23], it is shown that the basic features of Bohmian quantum gravity do not really depend on the factor ordering, although some ordering must be chosen to actually apply quantisation. Basead on that argument, it is common to apply only the trivial ordering in the quantization of the constrained Hamiltonian, like it is done in Ref. [23]. But the factor ordering ambiguity remains, so that we can ask ourselves: if the general features of that theory are invariant under a change of ordering...

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Section: Discussionsupporting

confidence: 85%

Section: The Ordering Problemmentioning

confidence: 95%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Bouncing and cyclic quantum primordial universes and the ordering problem

Torres¹,

Fabris²,

Piattella³

2020

Class. Quantum Grav.

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“…On the other hand, applying Bohmian causal interpretation of quantum mechanics to quantum cosmology has several positive aspects compared to the copenhagen interpretation [10][11][12]. For example, it provides time evolution of dynamical variables via Bohmian trajectories, whether the malfunction depends or not on the time variable.…”

Section: Introductionmentioning

confidence: 99%

Quantum cosmology with varying speed of light and Bohmian trajectories

Shojai

Molladavoudi

2007

Gen Relativ Gravit

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The classical trajectories for FLRW universe with varying speed of light are obtained for the cases in which the cosmological constant depends or not depend on the velocity of light. The theory is then quantized and the corresponding WDW equation is solved. It is shown that the method of causal interpretation of Bohm can be applied successfully to the theory. Finally the Bohmian trajectories are obtained and compared with the classical ones

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The Quantum Potential in Gravity and Cosmology

Licata

Fiscaletti

2013

SpringerBriefs in Physics

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Quantum cosmology: how to interpret and obtain results

Cited by 8 publications

References 0 publications

Bouncing and cyclic quantum primordial universes and the ordering problem

Bouncing and cyclic quantum primordial universes and the ordering problem

Quantum cosmology with varying speed of light and Bohmian trajectories

The Quantum Potential in Gravity and Cosmology

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