Quantum unitary evolution of linearly polarized {\sbb S}^1\times {\sbb S}^2 and {\sbb S}^3 Gowdy models coupled to massless scalar fields

G, J Fernando Barbero; Vergel, Daniel Gómez; Villaseñor, Eduardo J. S.

doi:10.1088/0264-9381/25/8/085002

Cited by 22 publications

(20 citation statements)

References 25 publications

(80 reference statements)

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“…In addition, we proved that with our choice of variables, the time evolution can be implemented by a unitary operator. This result extends the literature [21][22][23][24][25][26][27][28][29][30][31][32][33] by introducing for the first time a set of special canonical variables for a multiple component system coupled by quadratic terms in the Hamiltonian for which the time evolution is unitary. All these results were accomplished using adiabatic invariants, which proved essential to understand the UV asymptotic behavior of the solutions.…”

Section: Discussionsupporting

confidence: 76%

“…This result extends the work done in Ref. [21] (for particular examples, see also [22][23][24][25][26][27][28][29][30][31][32][33]) by showing a concrete example of choice of variables and initial conditions which leads to a unitary implementation of the time evolution for quantum fields interacting through a quadratic term in the Hamiltonian.…”

Section: Introductionsupporting

confidence: 83%

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Quantum cosmological perturbations of multiple fluids

2016

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The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid).PACS numbers: 98.80. Es, 98.80.Jk

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Section: Discussionsupporting

confidence: 76%

Section: Introductionsupporting

confidence: 83%

Quantum cosmological perturbations of multiple fluids

2016

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“…First, the classical models were addressed in [38], showing that, in these cases, the local gravitational DoF can also be parametrized by a single scalar field, namely an axisymmetric field in S 2 . Then, following a procedure similar to the one introduced by Corichi, Cortez, and Mena Marugán, a Fock quantization with unitary dynamics was obtained [39]. In particular, a time-dependent scaling of the original field is again involved, now of the form φ → √ sin tφ.…”

Section: Gowdy Modelsmentioning

confidence: 99%

A Brief Overview of Results about Uniqueness of the Quantization in Cosmology

2021

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The purpose of this review is to provide a brief overview of recent conceptual developments regarding possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems. These criteria impose certain conditions on the representation of a group of physically relevant linear transformations. Generally, this group contains any existing symmetry of the spatial sections. These symmetries may or may not be sufficient for the purpose of uniqueness and may have to be complemented with other remaining symmetries that affect the time direction or with dynamical transformations that are, in fact, not symmetries. We discuss the extent to which a unitary implementation of the resulting group suffices to fix the quantization—a demand that can be seen as a weaker version of the requirement of invariance. In particular, a strict invariance under certain transformations may eliminate some physically interesting possibilities in the passage to the quantum theory. This is the first review in which this unified perspective is adopted to discuss otherwise different uniqueness criteria proposed either in homogeneous loop quantum cosmology or in the Fock quantization of inhomogeneous cosmologies.

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“…An analysis similar to the one that we have presented above has also been performed to achieve a unique quantum description of the linearly-polarized Gowdy S 1 × S 2 and S 3 cosmological models [25,26]. For that purpose, the result of uniqueness has been extended to axisymmetric fields with a time dependent mass equal to (1 + csc 2 t)/4 on S 2 , case which describes the field sector (after a suitable scaling) of the Gowdy models with the spatial topology of a three-handle and a three-sphere [24][25][26]. The uniqueness proven for the Gowdy models has also been generalized to scalar fields with arbitrary mass terms 16 on S 1 (and naturally continued to axisymmetric fields on the two-sphere) [12].…”

Section: )mentioning

confidence: 99%

“…Specifically, for Gowdy cosmologies with the topology of a three-torus, the wave equation corresponds to a scalar field with time dependent mass propagating in a static (1 + 1)-dimensional fictitious spacetime, for which the spatial manifold Σ is a circle [12,[19][20][21][22][23]. For the threesphere and the three-handle, which are the remaining two possible spatial topologies in the Gowdy models, the local gravitational degrees of freedom are described by an axisymmetric KG field with time dependent mass in a static (2 + 1)-dimensional auxiliary spacetime, such that the spatial slices are two-spheres [24][25][26]. Let us recall, in addition, that in non-stationary scenarios like those encountered in cosmology, it is customary to scale the field configurations by time varying functions when one allows that part of its evolution be assigned to the time dependent spacetime in which the propagation takes place.…”

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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 evolution of linearly polarized {\sbb S}^1\times {\sbb S}^2 and {\sbb S}^3 Gowdy models coupled to massless scalar fields

Cited by 22 publications

References 25 publications

Quantum cosmological perturbations of multiple fluids

Quantum cosmological perturbations of multiple fluids

A Brief Overview of Results about Uniqueness of the Quantization in Cosmology

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

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