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キーワード:
General Relativity and Quantum Cosmology, gr-qc,Astrophysics, Cosmology and Extragalactic Astrophysics, astro-ph.CO,High Energy Physics - Theory, hep-th
要旨:
We give a general procedure, in the group field theory (GFT) formalism for
quantum gravity, for constructing states that describe macroscopic, spatially
homogeneous universes. These states are close to coherent (condensate) states
used in the description of Bose-Einstein condensates. The condition on such
states to be (approximate) solutions to the quantum equations of motion of GFT
is used to extract an effective dynamics for homogeneous cosmologies directly
from the underlying quantum theory. The resulting description in general gives
nonlinear and nonlocal equations for the 'condensate wavefunction' which are
analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We
show the general form of the effective equations for current quantum gravity
models, as well as some concrete examples. We identify conditions under which
the dynamics becomes linear, admitting an interpretation as a
quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB)
approximation in the case of a kinetic term that includes a Laplace-Beltrami
operator. For isotropic states, this approximation reproduces the classical
Friedmann equation in vacuum with positive spatial curvature. We show how the
formalism can be consistently extended from Riemannian signature to Lorentzian
signature models, and discuss the addition of matter fields, obtaining the
correct coupling of a massless scalar in the Friedmann equation from the most
natural extension of the GFT action. We also outline the procedure for
extending our condensate states to include cosmological perturbations. Our
results form the basis of a general programme for extracting effective
cosmological dynamics directly from a microscopic non-perturbative theory of
quantum gravity.
