An exactly solvable inflationary model
We discuss a model of gravity coupled to a scalar field that admits exact cosmological solutions displaying an inflationary behavior at early times and a power-law expansion at late times.
gr-qc↗
arXiv subjects
S. Mignemi
Publications and source records attributed to S. Mignemi.
Classical dynamics on curved Snyder space
We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parametrizing the solutions in terms of an auxiliary time variable, which is a function only of the physical time and of the energy and angular momentum of the particles, one can reduce the problem to the equivalent one in classical mechanics. We also discuss a relativistic extension of these results, and a generalization to the case in which the algebra is realized in flat space.
hep-th↗
Snyder dynamics in a Schwarzschild spacetime
We calculate the orbits of a particle in Schwarzschild spacetime, assuming that the dynamics is governed by a Snyder symplectic structure. With this assumption, the perihelion shift of the planets acquires an additional contribution with respect to the one predicted by general relativity. Moreover, the equivalence principle is violated. If one assumes that Snyder mechanics is valid also for macroscopic systems, these results impose strong constraints on the value of the coupling parameter of the Snyder model.
gr-qc↗
Classical dynamics on Snyder spacetime
We study the classical dynamics of a particle in Snyder spacetime, adopting the formalism of constrained Hamiltonian systems introduced by Dirac. We show that the motion of a particle in a scalar potential is deformed with respect to special relativity by terms of order βE^2. An important result is that in the relativistic Snyder model a consistent choice of the time variable must necessarily depend on the dynamics.
hep-th↗
Black brane solutions of Einstein-Maxwell-scalar theory with Liouville potential
We investigate the global properties of black brane solutions of a three-parameter Einstein-Maxwell model nonminimally coupled to a scalar with exponential potential. The black brane solutions of this model have recently been investigated because of their relevance for holography and for the AdS/condensed matter correspondence. We classify all the possible regular solutions and show that they exist only for a limited range of values of the parameters and that their asymptotic behavior either breaks hyperscaling invariance or has the form of a domain wall. We also write down some exact solutions in Schwarzschild coordinates.
gr-qc↗
Analytical mechanics of a relativistic particle in a positional potential
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be useful in the study of phenomenological models. Also the Dirac and Klein-Gordon equation differ from the standard formulation, with corrections of order (E-m)/m in the energy spectra.
physics.class-ph↗
Classical and quantum mechanics of the nonrelativistic Snyder model in curved space
The Snyder-de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature. It is an example of noncommutative spacetime admitting two fundamental scales besides the speed of light, and is invariant under the action of the de Sitter group. Here we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder-de Sitter (aSdS). By means of a nonlinear transformation relating the SdS phase space variables to canonical ones, we are able to investigate the classical and the quantum mechanics of a free particle and of an oscillator in this framework. As in their flat space limit, the SdS and aSdS models exhibit rather different properties. In the SdS case, a lower bound on the localization in position and momentum space arises, which is not present in the aSdS model. In the aSdS case, instead, a specific combination of position and momentum coordinates cannot exceed a constant value. We explicitly solve the classical and the quantum equations for the motion of the free particle and of the harmonic oscillator. In both the SdS and aSdS cases, the frequency of the harmonic oscillator acquires a dependence on the energy.
hep-th↗
Classical and quantum mechanics of the nonrelativistic Snyder model
The Snyder model is an example of noncommutative spacetime admitting a fundamental length scale $β$ and invariant under Lorentz transformations, that can be interpreted as a realization of the doubly special relativity axioms. Here, we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to three-dimensional Euclidean space. We discuss the classical and the quantum mechanics of a free particle in this framework, and show that they strongly depend on the sign of a coupling constant $λ$, appearing in the fundamental commutators and proportional to $β^2$. For example, if $λ$ is negative, momenta are bounded. On the contrary, for positive $λ$, positions and areas are quantized. We also give the exact solution of the harmonic oscillator equations both in the classical and the quantum case, and show that its frequency is energy dependent.
hep-th↗
Translation invariance and doubly special relativity
We propose a new interpretation of doubly special relativity based on the distinction between the momenta and the translation generators in its phase space realization. We also argue that the implementation of the theory does not necessarily require a deformation of the Lorentz symmetry, but only of the translation invariance.
gr-qc↗
Snyder-de Sitter model from two-time physics
We show that the symplectic structure of the Snyder model on a de Sitter background can be derived from two-time physics in seven dimensions and propose a Hamiltonian for a free particle consistent with the symmetries of the model.
gr-qc↗
The nonrelativistic limit of the Magueijo-Smolin model of deformed special relativity
We study the nonrelativistic limit of the motion of a classical particle in a model of deformed special relativity and of the corresponding generalized Klein-Gordon and Dirac equations, and show that they reproduce nonrelativistic classical and quantum mechanics, respectively, although the rest mass of a particle no longer coincides with its inertial mass. This fact clarifies the meaning of the different definitions of velocity of a particle available in DSR literature. Moreover, the rest mass of particles and antiparticles differ, breaking the CPT invariance. This effect is close to observational limits and future experiments may give indications on its effective existence.
hep-th↗
Lifetime of flying particles in canonical Doubly Special Relativity
We discuss the corrections to the lifetime of unstable elementary particles in some models of doubly special relativity. We assume that the speed of light is invariant and that the position coordinates transform in such a way to ensure the invariance of the deformed symplectic structure of phase space.
gr-qc↗
Extended uncertainty principle and the geometry of (anti)-de Sitter space
It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.
gr-qc↗
Exact solutions of dilaton gravity with (anti)-de Sitter asymptotics
We present a technique for obtaining spherically symmetric, asymptotically (anti)-de Sitter, black hole solutions of dilaton gravity with generic coupling to a Maxwell field, starting from exact asymptotically flat solutions and adding a suitable dilaton potential to the action.
gr-qc↗
Doubly special relativity and translation invariance
We propose a new interpretation of doubly special relativity (DSR) based on the distinction between the momentum and the translation generators in its phase space realization. We also argue that the implementation of DSR theories does not necessarily require a deformation of the Lorentz symmetry, but only of the translation invariance.
gr-qc↗
Triply special relativity from six dimensions
We show that the generalization of Doubly Special Relativity to a curved de Sitter background can be obtained starting from a six-dimensional spacetime on which quadratic constraints on position and momentum coordinates are imposed.
gr-qc↗
Doubly special relativity in de Sitter spacetime
We discuss the generalization of Doubly Special Relativity to a curved de Sitter background. The model has three observer-independent scales, the velocity of light $c$, the radius of curvature of the geometry $α$, and the Planck energy $κ$, and can be realized in a noncommutative position space. It is possible to construct a model exhibiting a duality for the interchange of positions and momenta together with the exchange of $α$ and $κ$.
gr-qc↗
The Magueijo-Smolin model of Deformed Special Relativity from five dimensions
It is known that the space of momenta of DSR can be identified with de Sitter space. In this paper, we discuss the relation of the noncanonical phase space of the Magueijo-Smolin model of DSR with the canonical 5-dimensional phase space in which the de Sitter space of momenta is embedded. We suggest that in analogy with the momentum variables, also the position variables should be constrained to lie on a null hypersurface of the five-dimensional space
gr-qc↗