scholarly journals Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Ángel Ballesteros ◽  
N. Rossano Bruno ◽  
Francisco J. Herranz
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Lie Algebras ◽  
Deformation Parameter ◽  
Planck Scale ◽  
Quantum Deformation ◽  
De Sitter ◽  
Planck Length ◽  
Unified Approach ◽  
Drinfel’D Double

Theκ-deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel’d-double and the Poisson–Lie structure underlying theκ-deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson–Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize theκ-Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of “duality” between the cosmological constant and the Planck scale is also envisaged.

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.

scholarly journals Prediction for the cosmological constant and constraints on SUSY GUTs in resummed quantum gravity

2018 ◽  
Vol 33 (29) ◽  
pp. 1830028
Author(s):  
B. F. L. Ward
Keyword(s):  
General Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Planck Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

Working in the context of the Planck scale cosmology formulation of Bonanno and Reuter, we use our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as [Formula: see text]. We show that SUSY GUT models are constrained by the closeness of this estimate to experiment. We also address various consistency checks on the calculation. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of [Formula: see text].

scholarly journals PROPOSAL OF A SECOND GENERATION OF QUANTUM-GRAVITY-MOTIVATED LORENTZ-SYMMETRY TESTS: SENSITIVITY TO EFFECTS SUPPRESSED QUADRATICALLY BY THE PLANCK SCALE

2003 ◽  
Vol 12 (09) ◽  
pp. 1633-1639 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA
Keyword(s):  
Quantum Gravity ◽  
Second Generation ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Cosmic Ray ◽  
Lorentz Symmetry ◽  
Planck Length ◽  
Satisfactory Description ◽  
Symmetry Tests ◽  
Quantum Spacetime

Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there are planned experiments with enough sensitivity to reveal these quantum-spacetime effects, if their magnitude is only linearly suppressed by the Planck length. Unfortunately, in some quantum-gravity scenarios even the strongest quantum-spacetime effects are suppressed by at least two powers of the Planck length, and many authors have argued that it would be impossible to test these quadratically-suppressed effects. I here observe that advanced cosmic-ray observatories and neutrino observatories can provide the first elements of an experimental programme testing the possibility of departures from Lorentz symmetry that are quadratically Planck-length suppressed.

scholarly journals Einstein–Heisenberg consistency condition interplay with cosmological constant prediction in resummed quantum gravity

2015 ◽  
Vol 30 (38) ◽  
pp. 1550206 ◽  
Author(s):  
B. F. L. Ward
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Promising Result ◽  
Consistency Condition ◽  
Planck Scale ◽  
Theory Of Relativity ◽  
Heisenberg Uncertainty Principle ◽  
Recent Success ◽  
Heisenberg Uncertainty ◽  
Frw Model

We argue that our recent success in using our resummed quantum gravity (RQG) approach to Einstein’s general theory of relativity, in the context of the Planck scale cosmology formulation of Bonanno and Reuter, to estimate the value of the cosmological constant [Formula: see text] supports the use of quantum mechanical consistency requirements to constrain the main uncertainty in that very promising result. This main uncertainty, which is due to the uncertainty in the value of the time [Formula: see text] at which the transition from the Planck scale cosmology to the FRW model occurs, is shown to be reduced, by requiring consistency between the Heisenberg uncertainty principle and the known properties of the solutions of Einstein’s equations, from four orders of magnitude to the level of a factor of [Formula: see text]. This lends more credibility to the overall RQG approach itself, in general, and to our estimate of [Formula: see text] in particular.

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 SYMMETRIES, SINGULARITIES AND THE DE-EMERGENCE OF SPACE

2008 ◽  
Vol 17 (03n04) ◽  
pp. 525-531 ◽  
Author(s):  
THIBAULT DAMOUR ◽  
HERMANN NICOLAI
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Recent Work ◽  
Lie Algebras ◽  
Planck Scale ◽  
Space Time ◽  
Moody Algebra ◽  
Type Analysis ◽  
Infinite Dimensional ◽  
Background Independence

Recent work has revealed intriguing connections between a Belinsky–Khalatnikov–Lifshitz-type analysis of spacelike singularities in general relativity and certain infinite-dimensional Lie algebras, particularly the "maximally extended" hyperbolic Kac–Moody algebra E10. In this essay we argue that these results may lead to an entirely new understanding of the (quantum) nature of space(–time) at the Planck scale, and hence — via an effective "de-emergence" of space near the singularity — to a novel mechanism for achieving background independence in quantum gravity.

scholarly journals Midisuperspace foam and the cosmological constant

2021 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
Initial Data ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Spherical Symmetry ◽  
Planck Scale ◽  
Stationary States ◽  
Infinite Class ◽  
Probability Current ◽  
Spacetime Foam ◽  
Large Quantum

Abstract Wheeler's conjectured "spacetime foam" -- large quantum fluctuations of spacetime at the Planck scale -- could have important implications for quantum gravity, perhaps even explaining why the cosmological constant seems so small. Here I explore this problem in a midisuperspace model consisting of metrics with local spherical symmetry. Classically, an infinite class of ``foamy'' initial data can be constructed, in which cancellations between expanding and contracting regions lead to a small average expansion even if Λ is large. Quantum mechanically, the model admits corresponding stationary states, for which the probability current is also nearly zero. These states appear to describe a self-reproducing spacetime foam with very small average expansion, effectively hiding the cosmological constant.

scholarly journals Holographic de Sitter spacetime and quantum corrections to the cosmological constant

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Shuichi Yokoyama
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Conformal Symmetry ◽  
Flow Equation ◽  
Vector Model ◽  
Quantum Corrections ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Dynamical Aspect

Abstract A dynamical aspect of quantum gravity on de Sitter spacetime is investigated by holography and the de Sitter/conformal field theory correspondence. We show that de Sitter spacetime emerges from a free Sp($N$) vector model by complexifying the ghost fields and course-graining them by flow equation in parallel to the imaginary axis. We confirm that the emergence of de Sitter spacetime is ensured by conformal symmetry. We also compute the quantum corrections to the cosmological constant up to the next-to-leading order of the $1/N$ expansion in a proposed holographic approach. As a result the sub-leading corrections have the opposite sign to the classical value. This implies that a quantum gravity on de Sitter spacetime is perturbatively stable and quantum effects make the universe flatter and the cosmological constant smaller.

scholarly journals Limits to Seeing High-Redshift Galaxies Due to Planck-Scale-Induced Blurring

2015 ◽  
Vol 11 (S319) ◽  
pp. 54-54
Author(s):  
Eric Steinbring
Keyword(s):  
Random Walk ◽  
Quantum Gravity ◽  
Gravity Model ◽  
High Redshift ◽  
Planck Scale ◽  
Holographic Principle ◽  
Planck Length ◽  
High Redshift Galaxies ◽  
Cosmological Distance ◽  
Redshift Galaxies

If spacetime is “foamy” travel along a lightpath must be subject to continual, random distance fluctuations ± δ l proportional to Planck length lP ~ 10−35 m (Lieu & Hillman 2003). Although each “kick” by itself is tiny, these may accumulate. Accounting for redshifted (bluer) emitted photons, over a cosmological distance L = (1+z)LC for co-moving distance LC, the resultant phase perturbations Δ φ = 2π δ l/λ at observed wavelength λ could grow independently of telescope diameter D to a maximum of Δφmax=(1+z)Δφ0 (Steinbring 2007) where Δφ0=2π a0 (lPα/λ)L1 - α follows Ng et al. (2003). Here a0 ~ 1 and α specifies the quantum-gravity model: 1/2 implies a random walk and 2/3 is consistent with the holographic principle; a vanishingly small ΔφP=Δφmax/[(1 + z) a0 (L/lP)1 - α]=2π lP/λ is approached when α=1.

Sign in / Sign up

Export Citation Format

Share Document