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.
