Backreaction of fermionic perturbations in the Hamiltonian of hybrid loop quantum cosmology

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

doi:10.1103/physrevd.98.063535

Cited by 10 publications

(46 citation statements)

References 41 publications

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“…A physically appealing possibility is to use this freedom, and hence remove (at least part of) the ambiguity, looking for annihilation and creation-like variables such that their Hamiltonian admits a quantum representation with good properties. In fact, there already exist some preliminary investigations about this issue in the technically simpler case of fermionic perturbations around flat FLRW spacetimes, within the hybrid LQC approach [31,53]. For a Dirac field in this cosmological scenario, one can also carry out a characterization of the annihilation and creation-like variables that define invariant vacua under the symmetry transformations of the system and display a unitarily implementable dynamics when considered on a classical background, all this while retaining a standard convention about the respective identification of particles and antiparticles [45].…”

Section: Further Specification Of Vacuamentioning

confidence: 99%

“…Nonetheless, if one imposes that the Hamiltonian that dictates the dynamics of the annihilation and creation operators in this fermionic case be well-defined on the vacuum, and therefore densely defined in Fock space, it is possible to prove that one arrives at further restrictions on the time dependence (through the homogeneous background variables) of the subdominant contributions of the coefficients that are analogous to f k and g k for the Dirac field. Moreover, these restrictions turn out to guarantee that certain contributions of the fermionic backreaction that affect the quantum evolution of the homogeneous geometry are well defined and finite without the need for any regularization [53].…”

Section: Further Specification Of Vacuamentioning

confidence: 99%

“…[50]). On the other hand, this choice of vacuum can be further restricted by imposing additional mathematical or physical requirements, for instance a well-defined quantum Hamiltonian or a regularizable backreaction [53]. The determination of this vacuum is of the greatest importance from a conceptual point of view, with implications for all kind of systems that evolve away from stationarity.…”

Section: Introductionmentioning

confidence: 99%

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The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology

2018

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We investigate the role played by the vacuum of the primordial fluctuations in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton potential is a mass term and the unperturbed quantum geometry is governed by the effective dynamics of Loop Quantum Cosmology. In this situation, the phenomenologically interesting solutions have a preinflationary regime where the kinetic energy of the inflaton dominates over the potential. For these kind of solutions, we show that the primordial power spectra depend strongly on the choice of vacuum. We study in detail the case of adiabatic states of low order and the non-oscillating vacuum introduced by Martín de Blas and Olmedo, all imposed at the bounce. The adiabatic spectra are typically suppressed at large scales, and display rapid oscillations with an increase of power at intermediate scales. In the non-oscillating vacuum, there is power suppression for large scales, but the rapid oscillations are absent. We argue that the oscillations are due to the imposition of initial adiabatic conditions in the region of kinetic dominance, and that they would also be present in General Relativity. Finally, we discuss the sensitivity of our results to changes of the initial time and other data of the model.

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Section: Further Specification Of Vacuamentioning

confidence: 99%

Section: Further Specification Of Vacuamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology

2018

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“…As we mentioned in the Introduction, the criteria of symmetry invariance and of unitary implementability of the quantum evolution have been successfully extended to select a unique preferred Fock representation for fermion fields in cosmological scenarios [46][47][48][49][50][51][52][53]. This and the uniqueness results here reviewed have been fruitfully exploited e.g.…”

Section: Discussionmentioning

confidence: 85%

“…Apart from addressing the uniqueness of the quantization of free real scalar fields in FLRW spacetimes [13][14][15][41][42][43], the criteria were successfully employed to remove the ambiguities in the quantization of free (test) KG fields minimally coupled to a de Sitter background [44], as well as in anisotropic Bianchi I spacetimes [45]. It is worth remarking that the criteria of invariance and of unitarity have also been fruitfully exploited to single out a unique preferred quantum description for fermion fields in cosmological scenarios [46][47][48][49][50][51][52][53].…”

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confidence: 99%

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

2020

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In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lemaître-Robertson-Walker, de Sitter, and Bianchi I spacetimes. These results are attained by imposing the criteria of symmetry invariance and of unitary implementability of the dynamics. This powerful combination of criteria allows not only to address the ambiguity in the representation of the canonical commutation relations, but also to single out a preferred set of fundamental variables. For the sake of clarity and completeness in the presentation (essentially as a background and complementary material), we first review the classical and quantum theories of a scalar field in globally hyperbolic spacetimes. Special emphasis is made on complex structures and the unitary implementability of symplectic transformations. * jacq@ciencias.unam.mx † mena@iem.cfmac.csic.es ‡ jvelhi@ubi.pt(2.1)By taking the direct sum of these two spaces, we get the complex vector space V + J ⊕ V − J , the elements of which can be written as (J turns out to be the same as V C , so that the complex vector spaces defined in Eq. (2.1) provide a splitting for the complexification of V . Besides, notice that every v in V can be decomposed asClearly, different complex structures will lead to distinct splittings for V C and, consequently, to different decompositions for v ∈ V . By extending the action of J from V to V C by complex linearity, we obtain that v + and v − are eigenvectors of J with eigenvalues i and −i,Given another complex structure, sayJ, its eigenvectors will satisfy relationships (2.2) with J replaced withJ. The eigenvectors ofJ and J are related byṽ. , x m , y 1 , . . . , y m )}. The standard (also called canonical) symplectic form is then. Equivalently, the standard symplectic form defines a skew-symmetric bilinear function on V [1], on C, and where we have used that Jv − = Jv + . A straightforward inspection shows that v, w J defines a Hermitian inner product on V + J ; that is,is a Hermitian inner product. This, together with the fact that any element of V + J is uniquely represented by an element of V (and vice versa), implies that the complex vector space V , with Hermitian inner product (2.7), and the complex vector space V + J , with Hermitian inner product (2.8), are (essentially) the same inner product spaces.B. The scalar field: Classical theory the unit function [see Eq. (2.11)]. Since observables on (S, Ω) can be obtained by taking linear combinations of products of natural observables Ω(φ, · ) and the unit function I (which provides the constant functions on S), the subspace 4 {I, Ω(φ, · ) | φ ∈ S} R of O qualifies as an admissible set of basic observables. This, together with the "naturalness and simplicity" of our choice, leads us to select the commented subspace as the set O 0 of fundamental (basic, or elementary) classical observables.By equipping the phase space (S, Ω) with a compatible complex structure J, the fi...

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Quantum unitary dynamics of a charged fermionic field and Schwinger effect

Álvarez-Domínguez

Garay

García-Heredia

et al. 2021

J. High Energ. Phys.

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In quantum field theory, particle creation occurs, in general, when an intense external field, such as an electromagnetic field, breaks time translational invariance. This leads to an ambiguity in the definition of the vacuum state. In cosmological backgrounds this ambiguity has been reduced by imposing that the quantization preserves the symmetries of the system and that the dynamics is unitarily implemented. In this work, we apply these requirements to the quantization of a massive charged fermionic field coupled to a classical time-dependent homogeneous electric field, extending previous studies done for a scalar field. We characterize the quantizations fulfilling the criteria above and we show that they form a unique equivalence class of unitarily related quantizations, which provide a well-defined number of created particles at all finite times.

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Backreaction of fermionic perturbations in the Hamiltonian of hybrid loop quantum cosmology

Cited by 10 publications

References 41 publications

The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology

The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology

Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

Quantum unitary dynamics of a charged fermionic field and Schwinger effect

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