Hybrid quantization of an inflationary model: The flat case

We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus. The quantization is carried out along the lines that were put forward by the authors in a previous work for spherical topology. The action of the system is truncated at second order in perturbations. The local gauge freedom is fixed at the classical level, although different gauges are discussed and shown to lead to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant quantities are considered. The reduced system is proven to admit a symplectic structure, and its dynamical evolution is dictated by a Hamiltonian constraint. Then, the background geometry is polymerically quantized, while a Fock representation is adopted for the inhomogeneities. The latter is selected by uniqueness criteria adapted from quantum field theory in curved spacetimes, which determine a specific scaling of the perturbations. In our hybrid quantization, we promote the Hamiltonian constraint to an operator on the kinematical Hilbert space. If the zero mode of the scalar field is interpreted as a relational time, a suitable ansatz for the dependence of the physical states on the polymeric degrees of freedom leads to a quantum wave equation for the evolution of the perturbations. Alternatively, the solutions to the quantum constraint can be characterized by their initial data on the minimum-volume section of each superselection sector. The physical implications of this model will be addressed in a future work, in order to check whether they are compatible with observations.Comment: 20 pages, no figures. v2: minor changes, in particular, abstract shortened, final discussion improve

Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in Loop Quantum Cosmology

We study the evolution of a homogeneous and isotropic spacetime whose spatial sections have three-torus topology, coupled to a massless scalar field with small scalar perturbations within loop quantum cosmology. We consider a proposal for the effective dynamics based on a previous hybrid quantization completed by us. Consequently, we introduce a convenient gauge fixing and adopt reduced canonical variables adapted to that hybrid quantum description. Besides, we keep backreaction contributions on the background coming from terms quadratic in the perturbations in the action of the system. We carry out a numerical analysis assuming that the inhomogeneities were in a massless vacuum state at distant past (where the initial data are set). At distant future, we observe a statistical amplification of the modes amplitude in the infrared region, as well as a phase synchronization arising from quantum gravity phenomena. A description of the perturbations in terms of the Mukhanov-Sasaki gauge invariants provides the same qualitative results. Finally, we analyze some consequences of the backreaction in our effective description.Comment: 15 pages, 9 figures. Accepted for publication in Phys. Rev.

A complete hybrid quantization in inhomogeneous cosmology

A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on the minimum volume section, and from this we construct the physical Hilbert space. Moreover, a perturbative study allows us to introduce small inhomogeneities. After gauge fixing, the inhomogeneous part of the system is reduced to a linear field theory. We then adopt a standard Fock representation to quantize these degrees of freedom. For the considered case of compact spatial topology, the requirements of: i) invariance under the spatial isometries, and ii) unitary implementation of the quantum dynamics, pick up a unique Fock representation and a particular set of canonical fields (up to unitary equivalence).Comment: 6 page

A uniqueness criterion for the Fock quantization of scalar fields with time dependent mass

A major problem in the quantization of fields in curved spacetimes is the ambiguity in the choice of a Fock representation for the canonical commutation relations. There exists an infinite number of choices leading to different physical predictions. In stationary scenarios, a common strategy is to select a vacuum (or a family of unitarily equivalent vacua) by requiring invariance under the spacetime symmetries. When stationarity is lost, a natural generalization consists in replacing time invariance by unitarity in the evolution. We prove that, when the spatial sections are compact, the criterion of a unitary dynamics, together with the invariance under the spatial isometries, suffices to select a unique family of Fock quantizations for a scalar field with time dependent mass.Comment: 11 pages, version accepted for publication in Classical and Quantum Gravit

Criteria for the determination of time dependent scalings in the Fock quantization of scalar fields with a time dependent mass in ultrastatic spacetimes

For Klein-Gordon fields, it is well known that there exist an infinite number of nonequivalent Fock representations of the canonical commutation relations and, therefore, of inequivalent quantum theories. A context in which this kind of ambiguities arises and prevents the derivation of robust results is, e.g., in the quantum analysis of cosmological perturbations. In these situations, typically, a suitable scaling of the field by a time dependent function leads to a description in an auxiliary static background, though the nonstationarity still shows up in a time dependent mass. For such a field description, and assuming the compactness of the spatial sections, we recently proved in three or less spatial dimensions that the criteria of a natural implementation of the spatial symmetries and of a unitary time evolution are able to select a unique class of unitarily equivalent vacua, and hence of Fock representations. In this work, we succeed to extend our uniqueness result to the consideration of all possible field descriptions that can be reached by a time dependent canonical transformation which, in particular, involves a scaling of the field by a function of time. This kind of canonical transformations modify the dynamics of the system and introduce a further ambiguity in its quantum description, exceeding the choice of a Fock representation. Remarkably, for any compact spatial manifold in less than four dimensions, we show that our criteria eliminate any possible nontrivial scaling of the field other than that leading to the description in an auxiliary static background. Besides, we show that either no time dependent redefinition of the field momentum is allowed or, if this may happen, the redefinition does not introduce any Fock representation that cannot be obtained by a unitary transformation.Comment: 37 pages. Modified title. Improved discussion concerning the spatial symmetry group. New section (section VI

Content Development for Leadership (SLO 23)

As the construction industry evolves, the curriculum that prepares future builders must change and account for new ideas and concepts as well. In September of 2020, the Construction Management department at the California Polytechnic State University (Cal Poly) gave the opportunity to five senior level students to assist them with research on how to develop content and programming for the five extra student learning outcomes and have it count toward their senior project. These five students, each being paired up with a student from CM 461, were asked to produce a study guide and survey questions for one of the five student learning outcomes. The purpose of this paper is to give a more in depth understanding of the logistics and process behind the whole senior project for the leadership student learning outcome. The study guide was inspired by a detailed literature review, collaboration and opinions of other students, and a reflection of students’ own professional experiences. The study guide covers leadership ideals and skills that a leader should have in order to be successful in the construction industry. The goal is to equip students with the tools that assure they will be great leaders and succeed in the construction industry

Ca II triplet spectroscopy of small magellanic cloud red giants. II. abundances for a sample of field stars

We have obtained metallicities of ∼360 red giant stars distributed in 15 Small Magellanic Cloud (SMC) fields from near-infrared spectra covering the Ca II triplet lines using the VLT + FORS2. The errors of the derived [Fe/H] values range from 0.09 to 0.35 dex per star, with a mean of 0.17 dex. The metallicity distribution (MD) of the whole sample shows a mean value of [Fe/H] = -1.00 ± 0.02, with a dispersion of 0.32 0.01, in agreement with global mean [Fe/H] values found in previous studies. We find no evidence of a metallicity gradient in the SMC. In fact, on analyzing the MD of each field, we derived mean values of [Fe/H] = -0.99 ± 0.08 and [Fe/H] = -1.02 ± 0.07 for fields located closer and farther than 4° from the center of the galaxy, respectively. In addition, there is a clear tendency for the field stars to be more metal-poor than the corresponding cluster they surround, independent of their positions in the galaxy and of the clusters' age. We argue that this most likely stems from the field stars being somewhat older and therefore somewhat more metal-poor than most of our clusters. © 2010. The American Astronomical Society.Fil: Parisi, Maria Celeste. Universidad Nacional de Cordoba. Observatorio Astronomico de Cordoba; ArgentinaFil: Geisler, Doug. Universidad de Concepción; ChileFil: Grocholski, A. J.. University of Florida; Estados Unidos. Space Telescope Science Institute; Estados UnidosFil: Claria Olmedo, Juan Jose. Universidad Nacional de Cordoba. Observatorio Astronomico de Cordoba; ArgentinaFil: Sarajedini, A.. University of Florida; Estados Unido

Prescriptions in Loop Quantum Cosmology: A comparative analysis

Various prescriptions proposed in the literature to attain the polymeric quantization of a homogeneous and isotropic flat spacetime coupled to a massless scalar field are carefully analyzed in order to discuss their differences. A detailed numerical analysis confirms that, for states which are not deep in the quantum realm, the expectation values and dispersions of some natural observables of interest in cosmology are qualitatively the same for all the considered prescriptions. On the contrary, the amplitude of the wave functions of those states differs considerably at the bounce epoch for these prescriptions. This difference cannot be absorbed by a change of representation. Finally, the prescriptions with simpler superselection sectors are clearly more efficient from the numerical point of view.Comment: 18 pages, 6 figures, RevTex4-1 + BibTe