Scores of hesitant fuzzy elements revisited: “Was sind und was sollen”

[EN] This paper revolves around the notion of score for hesitant fuzzy elements, the constituent parts of hesitant fuzzy sets. Scores allow us to reduce the level of uncertainty of hesitant fuzzy sets to classical fuzzy sets, or to rank alternatives characterized by hesitant fuzzy information. We propose a rigorous and normative definition capable of encapsulating the characteristics of the most important scores introduced in the literature. We systematically analyse different types of scores, with a focus on coherence properties based on cardinality and monotonicity. The hesitant fuzzy elements considered in this analysis are unrestricted. The inspection of the infinite case is especially novel. In particular, special attention will be paid to the analysis of hesitant fuzzy elements that are intervals

The Theory of a Quantum Noncanonical Field in Curved Spacetimes

Much attention has been recently devoted to the possibility that quantum gravity effects could lead to departures from Special Relativity in the form of a deformed Poincar\`e algebra. These proposals go generically under the name of Doubly or Deformed Special Relativity (DSR). In this article we further explore a recently proposed class of quantum field theories, involving noncanonically commuting complex scalar fields, which have been shown to entail a DSR-like symmetry. An open issue for such theories is whether the DSR-like symmetry has to be taken as a physically relevant symmetry, or if in fact the "true" symmetries of the theory are just rotations and translations while boost invariance has to be considered broken. We analyze here this issue by extending the known results to curved spacetime under both of the previous assumptions. We show that if the symmetry of the free theory is taken to be a DSR-like realization of the Poincar\'e symmetry, then it is not possible to render such a symmetry a gauge symmetry of the curved physical spacetime. However, it is possible to introduce an auxiliary spacetime which allows to describe the theory as a standard quantum field theory in curved spacetime. Alternatively, taking the point of view that the noncanonical commutation of the fields actually implies a breakdown of boost invariance, the physical spacetime manifold has to be foliated in surfaces of simultaneity and the field theory can be coupled to gravity by making use of the ADM prescription.Comment: 9 pages, no figure

Linearized Treatment of Scalar perturbations in the Asymptotic Cosmological Model

In this paper the implications of a recently proposed phenomenological model of cosmology, the Asymptotic Cosmological Model (ACM), on the behavior of scalar perturbations are studied. Firstly we discuss new fits of the ACM at the homogeneous level, including fits to the Type Ia Supernovae UNION dataset, first CMB peak of WMAP5 and BAOs. The linearized equations of scalar perturbations in the FRW metric are derived. A simple model is used to compute the CMB temperature perturbation spectrum. The results are compared with the treatment of perturbations in other approaches to the problem of the accelerated expansion of the universe.Comment: 14 pages, 5 figures. Presentation in sections 2 and 3 clarified, references added. Final version to appear in Astroparticle Physic

Interpretation of neutrino oscillations based on new physics in the infrared

An interpretation of neutrino oscillations based on a modification of relativistic quantum field theory at low energies, without the need to introduce a neutrino mass, is seen to be compatible with all observations.Comment: 4 pages, no figures, final version to appear in JHEP, several changes in the presentation (including title), main conclusions are not modifie

An extension of the cosmological standard model with a bounded Hubble expansion rate

The possibility of having an extension of the cosmological standard model with a Hubble expansion rate $H$ constrained to a finite interval is considered. Two periods of accelerated expansion arise naturally when the Hubble expansion rate approaches to the two limiting values. The new description of the history of the universe is confronted with cosmological data and with several theoretical ideas going beyond the standard cosmological model.Comment: 10 pages, 4 figures. Minor revisio

Probing the quantum-gravity realm with slow atoms

For the study of Planck-scale modifications of the energy-momentum dispersion relation, which had been previously focused on the implications for ultrarelativistic (ultrafast) particles, we consider the possible role of experiments involving nonrelativistic particles, and particularly atoms. We extend a recent result establishing that measurements of "atom-recoil frequency" can provide insight that is valuable for some theoretical models. And from a broader perspective we analyze the complementarity of the nonrelativistic and the ultrarelativistic regimes in this research area.Comment: LaTex, 13 page

An axiomatic approach to finite means

In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications