scholarly journals Geometric interpretation of Planck-scale-deformed co-products

2016 ◽  
Vol 41 ◽  
pp. 1660126 ◽  
Author(s):  
Iarley P. Lobo ◽  
Giovanni Palmisano
Keyword(s):  
Momentum Space ◽  
Isometry Group ◽  
Planck Scale ◽  
Geometric Interpretation ◽  
De Sitter ◽  
General Characterization ◽  
Dimensional Gravity ◽  
Composition Laws

For theories formulated with a maximally symmetric momentum space we propose a general characterization for the description of interactions in terms of the isometry group of the momentum space. The well known cases of [Formula: see text]-Poincaré-inspired and (2+1)-dimensional gravity-inspired composition laws both satisfy our condition. Future applications might include the proposal of a class of models based on momenta spaces with anti-de Sitter geometry.

scholarly journals Pathways to relativistic curved momentum spaces: de Sitter case study

2016 ◽  
Vol 25 (02) ◽  
pp. 1650027 ◽  
Author(s):  
Giovanni Amelino-Camelia ◽  
Giulia Gubitosi ◽  
Giovanni Palmisano
Keyword(s):  
Momentum Space ◽  
Hopf Algebras ◽  
Affine Connection ◽  
Planck Scale ◽  
Test Case ◽  
De Sitter ◽  
Group Manifold ◽  
The One ◽  
Natural Test

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: see text]-momentum space, with de Sitter (dS) metric and [Formula: see text]-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.

scholarly journals RELATIVE LOCALITY IN CURVED SPACETIME

2013 ◽  
Vol 28 (22) ◽  
pp. 1350101 ◽  
Author(s):  
JERZY KOWALSKI-GLIKMAN ◽  
GIACOMO ROSATI
Keyword(s):  
Momentum Space ◽  
Planck Scale ◽  
De Sitter ◽  
Curved Spacetime ◽  
Soccer Ball ◽  
The Core ◽  
Core Feature ◽  
Space Curvature ◽  
Curvature Deformation ◽  
Ball Problem

In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a nontrivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are present. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (de Sitter) spacetimes, relying on their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with κ-Poincaré momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.

scholarly journals Building models of inflation in no-scale supergravity

2020 ◽  
pp. 2030011
Author(s):  
John Ellis ◽  
Marcos A. G. García ◽  
Natsumi Nagata ◽  
Dimitri V. Nanopoulos ◽  
Keith A. Olive ◽  
...  
Keyword(s):  
Cold Dark Matter ◽  
Planck Scale ◽  
Neutrino Masses ◽  
De Sitter ◽  
Building Models ◽  
Scale Models ◽  
Cosmological Inflation ◽  
Text Model ◽  
Hilbert Action ◽  
Scalar Perturbations

After reviewing the motivations for cosmological inflation formulated in the formalism of supersymmetry, we argue that the appropriate framework is that of no-scale supergravity. We then show how to construct within this framework inflationary models whose predictions for the tilt in the spectrum of scalar perturbations, [Formula: see text], and the ratio, [Formula: see text], of tensor and scalar perturbations coincide with those of the [Formula: see text] model of inflation proposed by Starobinsky. A more detailed study of no-scale supergravity reveals a structure that is closely related to that of [Formula: see text] modifications of the minimal Einstein–Hilbert action for general relativity, opening avenues for constructing no-scale de Sitter and anti-de Sitter models by combining pairs of Minkowski models, as well as generalizations of the original no-scale Starobinsky models of inflation. We then discuss the phenomenology of no-scale models of inflation, including inflaton decay and reheating, and then the construction of explicit scenarios based on SU(5), SO(10) and string-motivated flipped SU(5)×U(1) GUT models. The latter provides a possible model of almost everything below the Planck scale, including neutrino masses and oscillations, the cosmological baryon asymmetry and cold dark matter, as well as [Formula: see text] and [Formula: see text].

scholarly journals COVARIANT REPRESENTATIONS OF THE DE SITTER ISOMETRY GROUP

2013 ◽  
Vol 28 (09) ◽  
pp. 1350033 ◽  
Author(s):  
ION I. COTĂESCU
Keyword(s):  
General Theory ◽  
Isometry Group ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Induced Representations ◽  
Covariant Representations ◽  
Sitter Spacetime ◽  
Technical Details ◽  
First Time

We show that the induced representations of the de Sitter isometry group proposed many years ago by Nachtmann are equivalent to those derived from our general theory of external symmetry. These methods complete each other leading to a coherent theory of covariant fields with spin on the de Sitter spacetime. Some technical details of these representations are presented here for the first time.

Kantowski-Sachs Cosmology, Weyl Geometry and Asymptotic Safety in Quantum Gravity

2020 ◽  
Author(s):  
Carlos Castro Perelman
Keyword(s):  
Black Hole ◽  
Planck Scale ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Exterior Region ◽  
Asymptotic Safety ◽  
Sign Change ◽  
Average Action ◽  
Black Hole Interior

A brief review of the essentials of Asymptotic Safety and the Renormalization Group (RG) improvement of the Schwarzschild Black Hole that removes the r = 0 singularity is presented. It is followed with a RG-improvement of the Kantowski-Sachs metric associated with a Schwarzschild black hole interior and such that there is no singularity at t = 0 due to the running Newtonian coupling G(t) (vanishing at t = 0). Two temporal horizons at t _- \simeq t_P and t_+ \simeq t_H are found. For times below the Planck scale t < t_P, and above the Hubble time t > t_H, the components of the Kantowski-Sachs metric exhibit a key sign change, so the roles of the spatial z and temporal t coordinates are exchanged, and one recovers a repulsive inflationary de Sitter-like core around z = 0, and a Schwarzschild-like metric in the exterior region z > R_H = 2G_o M. The inclusion of a running cosmological constant \Lambda (t) follows. We proceed with the study of a dilaton-gravity (scalar-tensor theory) system within the context of Weyl's geometry that permits to single out the expression for the classical potential V (\phi ) = \kappa\phi^4, instead of being introduced by hand, and find a family of metric solutions which are conformally equivalent to the (Anti) de Sitter metric. To conclude, an ansatz for the truncated effective average action of ordinary dilaton-gravity in Riemannian geometry is introduced, and a RG-improved Cosmology based on the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is explored.

BLACK HOLE QUANTIZATION, THERMODYNAMICS AND COSMOLOGICAL CONSTANT

2004 ◽  
Vol 13 (05) ◽  
pp. 885-898
Author(s):  
LI XIANG
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Planck Scale ◽  
Additional Term ◽  
Logarithmic Correction ◽  
De Sitter ◽  
Horizon Area ◽  
Constant Distance ◽  
The Universe

Bekenstein argues that the horizon area of a black hole has a constant distance spectrum. We investigate the effects of such a discrete spectrum on the thermodynamics of a Schwarzchild black hole (SBH) and a Schwarzchild–de Sitter black hole (SdBH), in terms of the time-energy uncertainty relation and Stefan–Boltzman law. For the massive SBH, a negative and logarithmic correction to the Bekenstein–Hawking entropy is obtained, as well as other authors by using other methods. As to the minimal hole near the Planck scale, its entropy is no longer proportional to the horizon area, but is of order of the mass of the hole. This is similar to an excited stringy state. The vanishing heat capacity of such a minimal black hole implies that it may be a remnant as the ground state of the evaporating hole. The properties of a SdBH are similar to the SBH, except for an additional term of square area associated with the cosmological constant. In order to maintain the validity of the Bekenstein–Hawking formula, the cosmological constant is strongly limited by the size of the biggest black hole in the universe. A relation associated with the cosmological constant, Planck area and the Stefan–Boltzman constant is obtained. The cosmological constant is not only related to the vacuum energy, but is also related to the thermodynamics.

scholarly journals GEOMETRIC MODULAR ACTION AND SPACETIME SYMMETRY GROUPS

2000 ◽  
Vol 12 (04) ◽  
pp. 475-560 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
OLAF DREYER ◽  
MARTIN FLORIG ◽  
STEPHEN J. SUMMERS
Keyword(s):  
Isometry Group ◽  
Three Dimensional ◽  
Algebraic Characterization ◽  
Symmetry Groups ◽  
De Sitter ◽  
Vacuum States ◽  
Point Transformations ◽  
Projective Representations ◽  
Modular Covariance

A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable additional conditions, these groups induce groups of point transformations on these space-times, which may be interpreted as symmetry groups. The consequences of this condition are studied in detail in application to two concrete space-times — four-dimensional Minkowski and three-dimensional de Sitter spaces — for which it is shown how this condition characterizes the states invariant under the respective isometry group. An intriguing new algebraic characterization of vacuum states is given. In addition, the logical relations between the condition proposed in this paper and the condition of modular covariance, widely used in the literature, are completely illuminated.

scholarly journals Anti-de Sitter momentum space

2015 ◽  
Vol 92 (2) ◽  
Author(s):  
Michele Arzano ◽  
Giulia Gubitosi ◽  
João Magueijo ◽  
Giovanni Amelino-Camelia
Keyword(s):  
Momentum Space ◽  
De Sitter

scholarly journals ANTI-DE SITTER GRAVITY FROM BF–CHERN–SIMONS–HIGGS THEORIES

2002 ◽  
Vol 17 (32) ◽  
pp. 2095-2103 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Isometry Group ◽  
Star Product ◽  
Constant Term ◽  
Higgs Potential ◽  
De Sitter ◽  
Potential Term ◽  
Higher Spin ◽  
Noncommutative Gravity ◽  
Chern Simons ◽  
Massless Fields

It is shown that an action inspired from a BF and Chern–Simons model, based on the AdS4 isometry group SO(3,2), with the inclusion of a Higgs potential term, furnishes the MacDowell–Mansouri–Chamseddine–West action for gravity, with a Gauss–Bonnet and cosmological constant term. The AdS4 space is a natural vacuum of the theory. Using Vasiliev's procedure to construct higher spin massless fields in AdS spaces and a suitable star product, we discuss the preliminary steps to construct the corresponding higher-spin action in AdS4 space representing the higher spin extension of this model. Brief remarks on noncommutative gravity are made.

scholarly journals Canonical quantization of the covariant fields on de Sitter space–times

2018 ◽  
Vol 33 (08) ◽  
pp. 1830007 ◽  
Author(s):  
Ion I. Cotaescu
Keyword(s):  
Isometry Group ◽  
Canonical Quantization ◽  
Principal Series ◽  
De Sitter Space ◽  
Fermion Mass ◽  
Dirac Field ◽  
De Sitter ◽  
Covariant Quantum ◽  
Covariant Representations ◽  
Casimir Operators

The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

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