Unique fermionic vacuum in de Sitter spacetime from hybrid quantum cosmology

Navascués, Beatriz Elizaga; Marugán, Guillermo A. Mena; Prado, Santiago

doi:10.1103/physrevd.101.123530

Cited by 3 publications

(16 citation statements)

References 45 publications

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“…Finally, it is worth noticing that Relation (111) can be used to show that the mode coefficients h k D of the resulting diagonal Hamiltonian, for each choice of fermionic variables characterized by a set of solutions to Equation (110) (for all k), acquire the form [75] 2h…”

Section: Hamiltonian Diagonalization In Hlqcmentioning

confidence: 99%

“…These are completely fixed in an iterative way if one introduces our ansatz in the interaction coefficients h k I of the fermionic Hamiltonian, and imposes that each contribution in inverse powers of ω k be equal to zero. Specifically, one then obtains [39,75]…”

Section: Asymptotic Diagonalizationmentioning

confidence: 99%

“…The general solution of this equation can be found by introducing a mode-dependent complex time T k = −2iω k η and the following change of variables [75]:…”

Section: Uniqueness Of the Vacuum: Minkowski And De Sitter Spacetimesmentioning

confidence: 99%

“…where C n are constants that are completely specified by a complicated nonlinear recurrence relation, with the initial value C 0 = mH −1 Λ [75]. We need not solve this relation, since the T k -dependence of the above asymptotic series, together with the known value of C 0 , is enough to restrict the associated expansion of v k in Equation (123) so that…”

Section: Uniqueness Of the Vacuum: Minkowski And De Sitter Spacetimesmentioning

confidence: 99%

“…In more detail, the Tricomi solution for v k selected by our criterion of asymptotic diagonalization leads, after several manipulations, to the following function ϕ k in Equation (123) [75]:…”

Section: Uniqueness Of the Vacuum: Minkowski And De Sitter Spacetimesmentioning

confidence: 99%

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Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

et al. 2020

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In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in non-stationary spacetimes, and present recent results obtained by us and our collaborators about well-motivated criteria capable to ensure the uniqueness in the selection of a vacuum up to unitary transformations, at least in certain situations of interest in cosmology. These criteria are based on two reasonable requirements. First, the invariance of the vacuum under the symmetries of the Dirac equations in the considered spacetime. These symmetries include the spatial isometries. Second, the unitary implementability of the Heisenberg dynamics of the annihilation and creation operators when the curved spacetime is treated as a fixed background. This last requirement not only permits the uniqueness of the Fock quantization but, remarkably, it also allows us to determine an essentially unique splitting between the phase space variables assigned to the background and the fermionic annihilation and creation variables. We first consider Dirac fields in 2 + 1 dimensions and then discuss the more relevant case of 3 + 1 dimensions, particularizing the analysis to cosmological spacetimes with spatial sections of spherical or toroidal topology. We use this analysis to investigate the combined, hybrid quantization of the Dirac field and a flat homogeneous and isotropic background cosmology when the latter is treated as a quantum entity, and the former as a perturbation. Specifically, we focus our study on a background quantization along the lines of loop quantum cosmology. Among the Fock quantizations for the fermionic perturbations admissible according to our criteria, we discuss the possibility of further restricting the choice of a vacuum by the requisite of a finite fermionic backreaction and, moreover, by the diagonalization of the fermionic contribution to the total Hamiltonian in the asymptotic limit of large wave numbers of the Dirac modes. Finally, we argue in support of the uniqueness of the vacuum state selected by the extension of this diagonalization condition beyond the commented asymptotic region, in particular proving that it picks out the standard Poincaré and Bunch–Davies vacua for fixed flat and de Sitter background spacetimes, respectively.

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Section: Hamiltonian Diagonalization In Hlqcmentioning

confidence: 99%

Section: Asymptotic Diagonalizationmentioning

confidence: 99%

“…The general solution of this equation can be found by introducing a mode-dependent complex time T k = −2iω k η and the following change of variables [75]:…”

Section: Uniqueness Of the Vacuum: Minkowski And De Sitter Spacetimesmentioning

confidence: 99%

Section: Uniqueness Of the Vacuum: Minkowski And De Sitter Spacetimesmentioning

confidence: 99%

Section: Uniqueness Of the Vacuum: Minkowski And De Sitter Spacetimesmentioning

confidence: 99%

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Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

et al. 2020

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Hybrid Loop Quantum Cosmology: An Overview

Navascués

Marugán

2021

Front. Astron. Space Sci.

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Loop Quantum Gravity is a nonperturbative and background independent program for the quantization of General Relativity. Its underlying formalism has been applied successfully to the study of cosmological spacetimes, both to test the principles and techniques of the theory and to discuss its physical consequences. These applications have opened a new area of research known as Loop Quantum Cosmology. The hybrid approach addresses the quantization of cosmological systems that include fields. This proposal combines the description of a finite number of degrees of freedom using Loop Quantum Cosmology, typically corresponding to a homogeneous background, and a Fock quantization of the field content of the model. In this review we first present a summary of the foundations of homogeneous Loop Quantum Cosmology and we then revisit the hybrid quantization approach, applying it to the study of Gowdy spacetimes with linearly polarized gravitational waves on toroidal spatial sections, and to the analysis of cosmological perturbations in preinflationary and inflationary stages of the Universe. The main challenge is to extract predictions about quantum geometry effects that eventually might be confronted with cosmological observations. This is the first extensive review of the hybrid approach in the literature on Loop Quantum Cosmology.

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Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

Cortez,

Navascués,

Marugán

et al. 2020

Preprint

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In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in non-stationary spacetimes, and present recent results obtained by us and our collaborators about well-motivated criteria capable to ensure the uniqueness in the selection of a vacuum up to unitary transformations, at least in certain situations of interest in cosmology. These criteria are based on two reasonable requirements. First, the invariance of the vacuum under the symmetries of the Dirac equations in the considered spacetime. These symmetries include the spatial isometries. Second, the unitary implementability of the Heisenberg dynamics of the annihilation and creation operators when the curved spacetime is treated as a fixed background. This last requirement not only permits the uniqueness of the Fock quantization but, remarkably, it also allows us to determine an essentially unique splitting between the phase space variables assigned to the background and the fermionic annihilation and creation variables. We first consider Dirac fields in 2+1 dimensions and then discuss the more relevant case of 3+1 dimensions, particularizing the analysis to cosmological spacetimes with spatial sections of spherical or toroidal topology. We use this analysis to investigate the combined, hybrid quantization of the Dirac field and a flat Friedmann-Lemaître-Robertson-Walker background cosmology when the latter is treated as a quantum entity, and the former as a perturbation. Specifically, we focus our study on a background quantization along the lines of loop quantum cosmology. Among the Fock quantizations for the fermionic perturbations admissible according to our criteria, we discuss the possibility of further restricting the choice of a vacuum by the requisite of a finite fermionic backreaction and, moreover, by the diagonalization of the fermionic contribution to the total Hamiltonian in the asymptotic limit of large wave numbers of the Dirac modes. Finally, we argue in support of the uniquess of the vacuum state selected by the extension of this diagonalization condition beyond the commented asymptotic region, in particular proving that it picks out the standard Poincaré and Bunch-Davies vacua for fixed flat and de Sitter background spacetimes, respectively.

show abstract

Unique fermionic vacuum in de Sitter spacetime from hybrid quantum cosmology

Cited by 3 publications

References 45 publications

Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

Hybrid Loop Quantum Cosmology: An Overview

Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

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