Quantum gravity with a positive cosmological constant

By Lee Smolin. 2002

195 citations recorded by the source corpus.

A quantum theory of gravity is described in the case of a positive cosmological constant in 3 + 1 dimensions. Both old and new results are described, which support the case that loop quantum gravity provides a satisfactory quantum theory of gravity. These include the existence of a ground state, discoverd by Kodama, which both is an exact solution to the constraints of quantum gravity and has a semiclassical limit which is deSitter spacetime. The long wavelength excitations of this state are studied and are shown to reproduce both gravitons and, when matter is included, quantum eld theory o n deSitter spacetime. Furthermore, one may derive directly from the Wheeler-deWitt equation corrections to the energy-momentum relations for matter elds of the form E 2 = p 2 +m 2 +l PlE 3 +::: where is a computable dimensionless constant. This may lead in the next few years to experimental tests of the theory. To study the excitations of the Kodama state exactly requires the use of the spin network representation, which is quantum deformed due to the cosmological constant. The theory may be developed within a single horizon, and the boundary states described exactly in terms of a boundary Chern-Simons theory. The Bekenstein bound is recovered and the N bound of Banks is given a background independent explanation. The paper is written as an introduction to loop quantum gravity, requiring no prior knowledge of the subject. The deep relationship between quantum gravity and topological eld theory is stressed throughout.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/988c89f37360ecbc1f46fffd1377aeaa0234bf80

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Citations in the corpus

The case for background independence (2005, background): “(16)See for example, [40] and [7] and references contained therein.”
An invitation to loop quantum gravity (2004, methodology): “One could easily study interactions among the excitations of candidate ground states such as those in [101, 102, 105, 106, 11].”
How far are we from the quantum theory of gravity (2003, methodology): “Indeed, as mentioned, several recent calculations indicate the presence of Planck scale corrections to the energy-momentum relations of the form of (2), effects that should be absent were the usual lorentz transformations exact symmetries[36, 37, 38].”
Quantum symmetry, the cosmological constant and Planck scale phenomenology (2003, background): “[8], one of us tried to approach the question of deformed dispersion relations by deriving one, for the simple case of a scalar field, from a state which is both an exact solution to all the quantum constraints of quantum gravity and has, at least naively, the full set of symmetries expected of the ”
An Analytical computation of asymptotic Schwarzschild quasinormal frequencies (2002, background): “While there are several open issues about the way quantum dynamics is currently handled in loop quantum gravity, the pretty kinematics—or perhaps the mathematically elegant attempts to understand de Sitter space in this framework (see [1])—can be separated and could well serve as a useful piece of o”
Quantum gravity and the standard model (2006, background): “Such ribbon graphs occur in the representation theory of quantum groups[7], and arise in topological field theories and in quantum gravity models with non-zero cosmological constant [8, 9].”