scholarly journals Investigation of Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case

2017 ◽  
Vol 95 (4) ◽  
Author(s):  
Iarley P. Lobo ◽  
Niccoló Loret ◽  
Francisco Nettel
Keyword(s):  
Finsler Geometry ◽  
Planck Scale ◽  
De Sitter ◽  
Curved Spacetime

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 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 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].

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 Dark energy and quantum gravity

2019 ◽  
Vol 28 (14) ◽  
pp. 1944018 ◽  
Author(s):  
Per Berglund ◽  
Tristan Hübsch ◽  
Djordje Minić
Keyword(s):  
Dark Energy ◽  
String Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Particle Physics ◽  
Dual Space ◽  
Planck Scale ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime

Realizing dark energy and the observed de Sitter spacetime in quantum gravity has proven to be obstructed in almost every usual approach. We argue that additional degrees of freedom of the left- and right-movers in string theory and a resulting doubled, noncommutatively generalized geometric formulation thereof can lead to an effective model of dark energy consistent with de Sitter spacetime. In this approach, the curvature of the canonically conjugate dual space provides for the dark energy inducing a positive cosmological constant in the observed spacetime, whereas the size of the above dual space is the gravitational constant in the same observed de Sitter spacetime. As a hallmark relation owing to a unique feature of string theory which relates short distances to long distances, the cosmological constant scale, the Planck scale and the effective TeV-sized particle physics scale must satisfy a see-saw-like formula — precisely the generic prediction of certain stringy cosmic brane type models.

Is dark matter and black hole cosmology an effect of Born’s reciprocal relativity theory?

2019 ◽  
Vol 97 (2) ◽  
pp. 198-209 ◽  
Author(s):  
Carlos Castro Perelman
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Phase Space ◽  
Lorentz Invariance ◽  
Finsler Geometry ◽  
Relativity Theory ◽  
Accelerated Expansion ◽  
Full Detail ◽  
Density Parameter ◽  
De Sitter

Born’s reciprocal relativity theory (BRRT), based on a maximal proper-force, maximal speed of light, and inertial and non-inertial observers, is re-examined in full detail. Relativity of locality and chronology are natural consequences of this theory, even in flat phase space. The advantage of BRRT is that Lorentz invariance is preserved and there is no need to introduce Hopf algebraic deformations of the Poincaré algebra, de Sitter algebra, nor non-commutative space–times. After a detailed study of the notion of generalized force, momentum, and mass in phase space, we explain that what one may interpret as “dark matter” in galaxies, for example, is just an effect of observing ordinary galactic matter in different accelerating frames of reference than ours. Explicit calculations are provided that explain these novel relativistic effects due to the accelerated expansion of the Universe, and which may generate the present-day density parameter value ΩDM ∼ 0.25 of dark matter. The physical origins behind the numerical coincidences in black hole cosmology are also explored. We finalize with a rigorous study of the curved geometry of (co)tangent bundles (phase space) within the formalism of Finsler geometry, and provide a short discussion on Hamilton spaces.

scholarly journals THERMODYNAMICS OF NONCOMMUTATIVE DE SITTER SPACE–TIME

2009 ◽  
Vol 18 (01) ◽  
pp. 159-171 ◽  
Author(s):  
B. VAKILI ◽  
N. KHOSRAVI ◽  
H. R. SEPANGI
Keyword(s):  
Uncertainty Principle ◽  
Vacuum Energy ◽  
Planck Scale ◽  
Heisenberg Algebra ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
Quantization Rule ◽  
Thermodynamical Properties ◽  
Noncommutative Parameter

We study the effects of noncommutativity of space–time geometry on the thermodynamical properties of the de Sitter horizon. We show that noncommutativity results in modifications in temperature, entropy and vacuum energy and that these modifications are of order of the Planck scale, suggesting that the size of the noncommutative parameter should be close to that of the Planck. In an alternative way to deal with noncommutativity, we obtain a quantization rule for the entropy. Since noncommutativity in space–time geometry modifies the Heisenberg algebra and introduces the general uncertainty principle, we also investigate the above problem in this framework.

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