Elimination of cosmological singularities in quantum cosmology by suitable operator orderings

Demaerel, Thibaut; Struyve, Ward

doi:10.1103/physrevd.100.046008

Cited by 8 publications

(20 citation statements)

References 34 publications

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“…Theoretical cosmologists typically employ a phenomenological description of matter's degree of freedom in the action (13). For example, a perfect fluid [9,[34][35][36][37][38][39][40][41][42][43][44][45][46], a Chaplygin gas [47][48][49][50], an anti-Chaplygin gas [51] or other phenomenological matters have been used. Because of the quantum nature of quantum cosmology, fundamental fields should theoretically characterize the matter content.…”

Section: Discussionmentioning

confidence: 99%

Resolution of challenging problems in quantum cosmology with electromagnetic radiation

Jalalzadeh

2022

Preprint

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We investigate the quantum cosmology of a closed spatially homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) minisuperspace model with electromagnetic radiation as matter content. We solve the corresponding Wheeler-DeWitt equation by utilizing Riemann's zeta function regularization method. We demonstrate that the regularized vacuum energy of the electromagnetic field can overcome factor ordering, boundary conditions, and singularity problems.

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Section: Discussionmentioning

confidence: 99%

Resolution of challenging problems in quantum cosmology with electromagnetic radiation

Jalalzadeh

2022

Preprint

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“…The last term in (10) is the action of the dust field. ρ and T represent the rest mass density and the dust field, respectively [7,11].…”

Section: The Time Issue In Quantum Gravity and Quantum Cosmologymentioning

confidence: 99%

“…Then starting from the action (10), one can show that the conjugate momentum of the dust field T is [7]…”

Section: The Time Issue In Quantum Gravity and Quantum Cosmologymentioning

confidence: 99%

“…In 2009, F. Amemiya and T. Koike based on the equation (2) (in the proper time coordinate) have shown that the initial singularity of the flat FRW universe can be avoided by the quantum effect [8]. There are also other works (see [9,10] and the related references there in) showing that the singularity can be avoided in the canonical quantum cosmology. In 2015, H. Maeda using the equation ( 2) studied the evolution of the quantum universe driven by the cosmological constant (dark energy) [11].…”

Section: Introductionmentioning

confidence: 99%

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Quantum cosmology of the flat universe via closed real-time path integral

Wang¹,

Wang²

2021

Preprint

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Understanding the evolution of the universe through the quantum cosmology approach is still not fully realized yet. Introducing the Brown-Kuchař dust field as the time variable, we studied the evolution of the quantum universe nonperturbatively by the closed real time path integral. We evaluated the influence functional of the massless scalar field coupled with the flat FRW universe. By setting the initial state of the spacetime as a Gaussian wave packet, we studied the evolution of the quantum universe. In the proper time coordinate, if the evolution of the universe is driven by the thermal radiation or the non-relativistic particles, we show a quantum spacetime can decohere to a classical spacetime. As the temperature of the thermal radiation decreases, the small quantum universe grows up to a larger classical universe. We show that whatever the form of the matter is, the classical trajectory of the universe is always consistent with the quantum evolution of the wave packet. We find that in different scenarios, the variation of the coherence is always consistent with the variation of the Gibbs entropy. We also studied the transition of the flat FRW universe starting from certain initial state of the spacetime. We illustrate that the transition probability is closely related to the Vilenkin's tunneling from nothing scenario. We show that the quantum universe can grow only when the initial state of the spacetime is distributed. We also show that under the larger cosmological constant or the higher radiation temperature a small universe has a higher chance of the transition to a bigger universe. Finally, we point out that in the proper time coordinate, the minimal coupling of the free massless field with the flat FRW spacetime can generally give rise to the memory characterized by non-Markovian correlations.

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“…For example, see Refs. [34,35,[42][43][44][45][46][47][48][49]. Additionally, for complementary mathematical aspects of the ordering problem, see for instance Refs.…”

Section: The Ordering Problemmentioning

confidence: 99%

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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Elimination of cosmological singularities in quantum cosmology by suitable operator orderings

Cited by 8 publications

References 34 publications

Resolution of challenging problems in quantum cosmology with electromagnetic radiation

Resolution of challenging problems in quantum cosmology with electromagnetic radiation

Quantum cosmology of the flat universe via closed real-time path integral

Bouncing and cyclic quantum primordial universes and the ordering problem

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