Quantum unitary dynamics in cosmological spacetimes

We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.Comment: 18 page

Uniqueness of the Fock quantization of the Gowdy T3T^3 model

After its reduction by a gauge-fixing procedure, the family of linearly polarized Gowdy $T^3$ cosmologies admit a scalar field description whose evolution is governed by a Klein-Gordon type equation in a flat background in 1+1 dimensions with the spatial topology of $S^1$, though in the presence of a time-dependent potential. The model is still subject to a homogeneous constraint, which generates $S^1$-translations. Recently, a Fock quantization of this scalar field was introduced and shown to be unique under the requirements of unitarity of the dynamics and invariance under the gauge group of $S^1$-translations. In this work, we extend and complete this uniqueness result by considering other possible scalar field descriptions, resulting from reasonable field reparameterizations of the induced metric of the reduced model. In the reduced phase space, these alternate descriptions can be obtained by means of a time-dependent scaling of the field, the inverse scaling of its canonical momentum, and the possible addition of a time-dependent, linear contribution of the field to this momentum. Demanding again unitarity of the field dynamics and invariance under the gauge group, we prove that the alternate canonical pairs of fieldlike variables admit a Fock representation if and only if the scaling of the field is constant in time. In this case, there exists essentially a unique Fock representation, provided by the quantization constructed by Corichi, Cortez, and Mena Marugan. In particular, our analysis shows that the scalar field description proposed by Pierri does not admit a Fock quantization with the above unitarity and invariance properties.Comment: 14 page

Quantum Gowdy T3T^3 model: A uniqueness result

Modulo a homogeneous degree of freedom and a global constraint, the linearly polarised Gowdy $T^3$ cosmologies are equivalent to a free scalar field propagating in a fixed nonstationary background. Recently, a new field parameterisation was proposed for the metric of the Gowdy spacetimes such that the associated scalar field evolves in a flat background in 1+1 dimensions with the spatial topology of $S^1$, although subject to a time dependent potential. Introducing a suitable Fock quantisation for this scalar field, a quantum theory was constructed for the Gowdy model in which the dynamics is implemented as a unitary transformation. A question that was left open is whether one might adopt a different, nonequivalent Fock representation by selecting a distinct complex structure. The present work proves that the chosen Fock quantisation is in fact unique (up to unitary equivalence) if one demands unitary implementation of the dynamics and invariance under the group of constant $S^1$ translations. These translations are precisely those generated by the global constraint that remains on the Gowdy model. It is also shown that the proof of uniqueness in the choice of complex structure can be applied to more general field dynamics than that corresponding to the Gowdy cosmologies.Comment: 28 pages, minor changes, version accepted for publication in Classical and Quantum Gravit

Massless scalar field in de Sitter spacetime: unitary quantum time evolution

We prove that, under the standard conformal scaling, a massless field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. This result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch-Davies vacuum.Comment: 23 pages. Typos corrected, matches published versio

Análisis sísmico en edificación de 4 pisos, incorporando al concreto partículas de plástico reciclado, en el Distrito de Parcona - Ica, 2022

Por medio del presente estudio se pretende analizar sísmicamente un edificio de 4 pisos, incorporando partículas de plástico al concreto, en el distrito de Parcona-ICA 2022, según los resultados aportar información de evaluó que se obtiene de realizar diseño de mezcla de concreto que tenga en su composición partículas de plástico para determinar su la resistencia del concreto, la elaboración y ensayos de probetas con la incorporación de plástico fueron en tres periodos (7 días, 14 días y 28 días), y la población está constituida por 36 probetas. En ese sentido este trabajo de investigación está comprendido por un diseño experimental, en donde el tipo se relaciona con la investigación aplicada, y posee un nivel explicativo, cuyo enfoque investigativo corresponde al a investigación cuantitativa. Debido a que se medirán los indicadores con valores numéricos. De acuerdo al desarrollo de la investigación se llegó al siguiente resultado, que el concreto con la incorporación de plástico reciclado influye en su resistencia a compresión de los elementos estructurales (columnas) de un edificio de 4 pisos, según a la proporción del material plástico reciclado incorporado al concreto, que para fines de nuestra investigación se utilizó (0%, 5%, 10%, 15%) de material plástico en el diseño de mezcla de concreto, cuyo ensayo se realizó a los 7, 14 y 28 días de curado. De acuerdo a los ensayos a compresión que se realizó en laboratorio, concluimos que la incorporación de partículas de plástico reciclado a la mezcla de concreto tuvo resultados desfavorables con relación al concreto patrón a los 28 días, obteniendo un f’c= 319.78kg/cm2 como el de mejor valor, (concreto con adición al 5%), contra un concreto patrón de f¨c= 347.96kg/cm2. De un diseño de mezcla de f´c= 210kg/cm2. Por lo que se aprecia un des favorecimiento a las propiedades mecánicas del concreto