Fermions in hybrid loop quantum cosmology

Navascués, Beatriz Elizaga; Marugán, Guillermo A. Mena; Martín-Benito, Mercedes

doi:10.1103/physrevd.96.044023

Cited by 16 publications

(70 citation statements)

References 73 publications

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“…In particular, the homogeneous part of these states, Γða; ϕÞ, where a generically denotes dependence on the homogeneous geometry, may be chosen as an exact solution to the, homogeneous, quantum FLRW model, and in this paper we will take it this way. However, let us comment that this choice is in principle not needed, and in fact one may consider other possibilities for Γ that incorporate the presence of some quantum backreaction of the perturbations onto the homogeneous sector of the model [19,63]. With this ansatz at hand, and provided that Γ is sufficiently peaked on the homogeneous geometry for all values of ϕ, then the imposition of the zero-mode of the Hamiltonian constraint leads to the requirement that the outcome of certain operators, acting exclusively on the Mukhanov-Sasaki and the tensor parts of the wave function, must be zero.…”

Section: A Hybrid Quantization Approachmentioning

confidence: 99%

Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology

2018

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Loop quantum cosmology has recently been applied in order to extend the analysis of primordial perturbations to the Planck era and discuss the possible effects of quantum geometry on the cosmic microwave background. Two approaches to loop quantum cosmology with admissible ultraviolet behavior leading to predictions that are compatible with observations are the so-called hybrid and dressed metric approaches. In spite of their similarities and relations, we show in this work that the effective equations that they provide for the evolution of the tensor and scalar perturbations are somewhat different. When backreaction is neglected, the discrepancy appears only in the time-dependent mass term of the corresponding field equations. We explain the origin of this difference, arising from the distinct quantization procedures. Besides, given the privileged role that the big bounce plays in loop quantum cosmology, e.g. as a natural instant of time to set initial conditions for the perturbations, we also analyze the positivity of the time-dependent mass when this bounce occurs. We prove that the mass of the tensor perturbations is positive in the hybrid approach when the kinetic contribution to the energy density of the inflaton dominates over its potential, as well as for a considerably large sector of backgrounds around that situation, while this mass is always nonpositive in the dressed metric approach. Similar results are demonstrated for the scalar perturbations in a sector of background solutions that includes the kinetically dominated ones; namely, the mass then is positive for the hybrid approach, whereas it typically becomes negative in the dressed metric case. More precisely, this last statement is strictly valid when the potential is quadratic for values of the inflaton mass that are phenomenologically favored.

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Section: A Hybrid Quantization Approachmentioning

confidence: 99%

Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology

2018

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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%

“…Two of these approaches do not modify the dispersion relations of the perturbations, providing in particular a proper ultraviolet behavior that is compatible with the observed power spectra. These are the hybrid [20,[23][24][25][26][27][28][29][30][31] and dressed metric approaches [21,[32][33][34][35][36][37]. Although there are plenty of similarities between these two approaches, the main distinctions follow from a slightly different strategy for the quantization of the perturbations [38].…”

Section: Introductionmentioning

confidence: 99%

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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“…within the Hybrid Quantization Approach [32] in order to deal with (both scalar and fermionic) perturbations in quantum cosmology (see, for instance, Refs. [100][101][102][103][104][105][106][107]).…”

Section: Discussionmentioning

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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Fermions in hybrid loop quantum cosmology

Cited by 16 publications

References 73 publications

Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology

Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to 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

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