Pathways to relativistic curved momentum spaces: de Sitter case study

© 2016 World Scientific Publishing Company Several arguments suggest that the Planck scale could be the characteristic scale of curvature of momentum space. As other recent studies, we assume that the metric of momentum space determines the condition of on-shellness while the momentum space affine connection governs the form of the law of composition of momenta. We show that the possible choices of laws of composition of momenta are more numerous than the possible choices of affine connection on a momentum space. This motivates us to propose a new prescription for associating an affine connection to momentum composition, which we compare to the one most used in the recent literature. We find that the two prescriptions lead to the same picture of the so-called (Formula presented.)-momentum space, with de Sitter (dS) metric and (Formula presented.)-Poincaré connection. We then show that in the case of “proper dS momentum space”, with the dS metric and its Levi–Civita connection, the two prescriptions are inequivalent. Our novel prescription leads to a picture of proper dS momentum space which is DSR-relativistic and is characterized by a commutative law of composition of momenta, a possibility for which no explicit curved momentum space picture had been previously found. This momentum space can serve as laboratory for the exploration of the properties of DSR-relativistic theories which are not connected to group-manifold momentum spaces and Hopf algebras, and is a natural test case for the study of momentum spaces with commutative, and yet deformed, laws of composition of momenta

Kinematics of particles with quantum-de Sitter-inspired symmetries

We present the first detailed study of the kinematics of free relativistic particles whose symmetries are compatible with the ones described by a quantum deformation of the de Sitter algebra, known as q–de Sitter Hopf algebra. In such algebra, the quantum deformation parameter is a function of the Planck length ℓ and the de Sitter radius H−1, such that when the Planck length vanishes, the algebra reduces to the de Sitter algebra, while when the de Sitter radius is sent to infinity, one recovers the κ-Poincaré Hopf algebra. In the first limit, the picture is that of a particle with trivial momentum space geometry moving on de Sitter spacetime; in the second one, the picture is that of a particle with de Sitter momentum space geometry moving on Minkowski spacetime. When both the Planck length and the inverse of the de Sitter radius are nonzero, effects due to spacetime curvature and nontrivial momentum space geometry are both present and affect each other. The particles’ motion is then described in a full phase-space picture. We find that redshift effects that are usually associated with spacetime curvature become energy dependent. Also, the energy dependence of the particles’ travel times that is usually associated with momentum space nontrivial properties is modified in a curvature-dependent way

Squeezing of scalar and tensor primordial perturbations generated by modified dispersion relations

In recent work we analyzed the evolution of primordial perturbations satisfying Planck-scale-modified dispersion relations and showed that there is no cosmological “squeezing” in the critical model that produces perturbations with a scale invariant spectrum. Nevertheless, the perturbations reenter the horizon as standing waves with the correct temporal phase because of the late-time decay of the momentum mode. Here we shed light on the absence of primordial squeezing by reexamining the problem in the dual rainbow frame, where c is set to 1, shifting the varying c effects elsewhere. In this frame gravity switches off at sub-Planckian wavelengths, so that the fluctuations behave as if they were in Minkowski spacetime. This is ultimately why they are not squeezed. However, away from the critical model squeezing does occur if the fluctuations spectrum is red, as is the case for scalar perturbations. Should the primordial gravity waves have a blue spectrum, we predict that they might not reenter the horizon as standing waves, because the momentum mode would be enhanced in the primordial phase

Quantum groups, non-commutative Lorentzian spacetimes and curved momentum spaces

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Using CMB data to constrain non-isotropic Planck-scale modifications to Electrodynamics

We develop a method to constrain non-isotropic features of Cosmic Microwave Background (CMB) polarization, of a type expected to arise in some models describing quantum gravity effects on light propagation. We describe the expected signatures of this kind of anomalous light propagation on CMB photons, showing that it will produce a non-isotropic birefringence effect, i.e. a rotation of the CMB polarization direction whose observed amount depends in a peculiar way on the observation direction. We also show that the sensitivity levels expected for CMB polarization studies by the \emph{Planck} satellite are sufficient for testing these effects if, as assumed in the quantum-gravity literature, their magnitude is set by the minute Planck length.Comment: 18 pages, 4 figures, 2 table

Cosmological birefringence constraints from CMB and astrophysical polarization data

Cosmological birefringence is a rotation of the polarization plane of photons coming from sources of astrophysical and cosmological origin. The rotation can also depend on the energy of the photons and not only on the distance of the source and on the cosmological evolution of the underlying theoretical model. In this work, we constrain few selected models for cosmological birefringence, combining CMB and astrophysical data at radio, optical, X and gamma wavelengths, taking into account the specific energy and distance dependences.Comment: 12 pages, 2 figure

Double quantization

In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties. A possible way to take into account these quantum effects is through a noncommutativity of spacetime coordinates. In the literature, there is not a clear way to describe at the same time a noncommutativity of spacetime and the phase-space noncommutativity of quantum mechanics. In this paper we address this issue by constructing a Drinfel''d twist in phase space which deals with both quantizations. This method can be applied to a noncommutativity which involves only space, leaving time aside. We apply our construction to the so-called ?-Minkowski and R?3 noncommutative spaces. © 2022 authors. Published by the American Physical Society

Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions

Producción CientíficaCurved momentum spaces associated to the k-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated to the k-deformation with non-vanishing cosmological constant. The k-de Sitter and k-Anti-de Sitter curved momentum spaces are separately analysed, and they turn out to be, respectively, half of the (6+1)-dimensional de Sitter space and half of a space with SO(4, 4) invariance. Such spaces are made of the momenta associated to spacetime translations and the ‘hyperbolic’ momenta associated to boost transformations. The known k-Poincaré curved momentum space is smoothly recovered as the vanishing cosmological constant limit from both of the constructions.Ministerio de Economía, Industria y Competitividad (projects MTM2013-43820-P / MTM2016-79639-P)Junta de Castilla y León (projects BU278U14 / VA057U16)European Cooperation in Science and Technology (Action MP1405 QSPACE

Primordial standing waves

We consider the possibility that the primordial fluctuations (scalar and tensor) might have been standing waves at their moment of creation, whether or not they had a quantum origin. We lay down the general conditions for spatial translational invariance, and isolate the pieces of the most general such theory that comply with, or break translational symmetry. We find that, in order to characterize statistically translationally invariant standing waves, it is essential to consider the correlator ⟨c0(k)c0(k′)⟩ in addition to the better known ⟨c0(k)c†0(k′)⟩ [where c0(k) are the complex amplitudes of traveling waves]. We then examine how the standard process of “squeezing” (responsible for converting traveling waves into standing waves while the fluctuations are outside the horizon) reacts to being fed primordial standing waves. For translationally invariant systems only one type of standing wave, with the correct temporal phase (the “sine wave”), survives squeezing. Primordial standing waves might therefore be invisible at late times—or not—depending on their phase. Theories with modified dispersion relations behave differently in this respect, since only standing waves with the opposite temporal phase survive at late times

The Use of Six Sigma to Assess Two Prostheses for Immediate Breast Reconstruction

Breast reconstruction is fundamental and urgent for patients in order to avoid future psychological and physical issues. That’s why immediate breast reconstruction has been requested increasingly in the last years. In this study two prosthesis with different structures and properties were compared according the aesthetic appearance (BREAST-Q© was employed) and five complications (seroma, hematoma, infections, dehiscence and red breast syndrome). The overall population was composed by 56 patients: 24 received a Tutomesh prosthesis and 32 received a Surgimend prosthesis. The DMAIC (define, measure, analyse, improve and control) cycle was implemented as a problem-solving strategy of the Six Sigma to compare the prostheses. While statistically significant difference between the two groups wasn’t found according to the overall BREAST-Q© (p-value = 0.674), the number of complications of the two groups resulted statistically different (p-value of chi-square test less than 0.001). Although it is not possible to understand from this study the reasons of the differences between the complications, this research proved that Surgimend and Tutomesh prostheses can be both implanted safely for immediate breast reconstruction since the higher costs of Surgimend could be neutralized with its lower hospitalization compared to Tutomesh. © 2021, Springer Nature Switzerland AG