The quantum structure of space-time at the Planck scale and quantum fields

 ,Sergio Doplicher, Klaus Fredenhagen, John E. Roberts


(Submitted on 5 Mar 2003)

We propose uncertainty relations for the different coordinates of space-time events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Space-time is then discussed where the commutation relations exactly implement our uncertainty relations. 

We outline the definition of free fields and interactions over QST and take the first steps to adapting the usual perturbation theory. The quantum nature of the underlying spacetime replaces a local interaction by a specific nonlocal effective interaction in the ordinary Minkowski space. A detailed study of interacting QFT and of the smoothing of ultraviolet divergences is deferred to a subsequent paper. 

In the classical limit where the Planck length goes to zero, our Quantum Spacetime reduces to the ordinary Minkowski space times a two component space whose components are homeomorphic to the tangent bundle TS^2 of the 2-sphere. The relations with Connes' theory of the standard model will be studied elsewhere

 

https://arxiv.org/abs/hep-th/0303037

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Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant 

Authors: Riess, Adam G.; Filippenko, Alexei V.; Challis, Peter; Clocchiatti, Alejandro; Diercks, Alan; Garnavich, Peter M.; Gilliland, Ron L.; Hogan, Craig J.; Jha, Saurabh; Kirshner, Robert P.; Leibundgut, B.; Phillips, M. M.; Reiss, David; Schmidt, Brian P.; Schommer, Robert A.; Smith, R. Chris; Spyromilio, J.; Stubbs, Christopher; Suntzeff, Nicholas B.; Tonry, John

Bibliographic Code: 1998AJ....116.1009R

Abstract

We present spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.62 ≥ z ≥ 0.16. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-z Supernova Search Team and recent results by Riess et al., this expanded set of 16 high-redshift supernovae and a set of 34 nearby supernovae are used to place constraints on the following cosmological parameters: the Hubble constant (H0), the mass density (ΩM), the cosmological constant (i.e., the vacuum energy density, Ωλ), the deceleration parameter (q0), and the dynamical age of the universe (t0). The distances of the high-redshift SNe Ia are, on average, 10%-15% farther than expected in a low mass density (ΩM = 0.2) universe without a cosmological constant. Different light curve fitting methods, SN Ia subsamples, and prior constraints unanimously favor eternally expanding models with positive cosmological constant (i.e., Ωλ > 0) and a current acceleration of the expansion (i.e., q0 < 0). With no prior constraint on mass density other than Omega_M >= 0, the spectroscopically confirmed SNe Ia are statistically consistent with q0 < 0 at the 2.8 σ and 3.9 σ confidence levels, and with Ωλ > 0 at the 3.0 σ and 4.0 σ confidence levels, for two different fitting methods, respectively. Fixing a ``minimal'' mass density, Omega_M = 0.2, results in the weakest detection, Ωλ > 0 at the 3.0 σ confidence level from one of the two methods. For a flat universe prior (ΩM + Ωλ = 1), the spectroscopically confirmed SNe Ia require Ωλ > 0 at 7 σ and 9 σ formal statistical significance for the two different fitting methods. A universe closed by ordinary matter (i.e., ΩM = 1) is formally ruled out at the 7 σ to 8 σ confidence level for the two different fitting methods. We estimate the dynamical age of the universe to be 14.2 +/- 1.7 Gyr including systematic uncertainties in the current Cepheid distance scale. We estimate the likely effect of several sources of systematic error, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. Presently, none of these effects appear to reconcile the data with Ωλ = 0 and q0 >= 0.

http://www.stsci.edu/~ariess/documents/1998.pdf

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Dark energy as a kinematic effect

Hendrick Jennen_Sao Paulo, IFT 


Abstract 
Observations during the last three decades have confirmed that the universe momentarily expands at an accelerated rate, which is assumed to be driven by dark energy whose origin remains unknown. The minimal manner of modelling dark energy is to include a positive cosmological constant in Einstein’s equations, whose solution in vacuum is de Sitter space. This indicates that the large-scale kinematics of spacetime is approximated by the de Sitter group SOp1, 4q rather than the Poincaré group ISOp1, 3q. In this thesis we take this consideration to heart and conjecture that the group governing the local kinematics of physics is the de Sitter group, so that the amount to which it is a deformation of the Poincaré group depends pointwise on the value of a nonconstant cosmological function. With the objective of constructing such a framework we study the Cartan geometry in which the model Klein space is at each point a de Sitter space for which the combined set of pseudoradii forms a nonconstant function on spacetime. We find that the torsion receives a contribution that is not present for a cosmological constant. Invoking the theory of nonlinear realizations we extend the class of symmetries from the Lorentz group SOp1, 3q to the enclosing de Sitter group. Subsequently, we find that the geometric structure of teleparallel gravity— a description for the gravitational interaction physically equivalent to general relativity— is a nonlinear Riemann–Cartan geometry. This finally inspires us to build on top of a de Sitter–Cartan geometry with a cosmological function a generalization of teleparallel gravity that is consistent with a kinematics locally regulated by the de Sitter group. The cosmological function is given its own dynamics and naturally emerges nonminimally coupled to the gravitational field in a manner akin to teleparallel dark energy models or scalar-tensor theories in general relativity. New in the theory here presented, the cosmological function gives rise to a kinematic contribution in the deviation equation for the world lines of adjacent free-falling particles. While having its own dynamics, dark energy manifests itself in the local kinematics of spacetime.