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Register a new userPregeometry and euclidean quantum gravity
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Christof Wetterich
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Einsteins general relativity can emerge from pregeometry, with the metric composed of more fundamental fields. We formulate euclidean pregeometry as a $SO(4)$ - Yang-Mills theory. In addition to the gauge fields we include a vector field in the vector representation of the gauge group. The gauge - and diffeomorphism - invariant kinetic terms for these fields permit a well-defined euclidean functional integral, in contrast to metric gravity with the Einstein-Hilbert action. The propagators of all fields are well behaved at short distances, without tachyonic or ghost modes. The long distance behavior is governed by the composite metric and corresponds to general relativity. In particular, the graviton propagator is free of ghost or tachyonic poles despite the presence of higher order terms in a momentum expansion of the inverse propagator. This pregeometry seems to be a valid candidate for euclidean quantum gravity, without obstructions for analytic continuation to a Minkowski signature of the metric.
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In pregeometry a metric arises as a composite object at large distances. For short distances we investigate a Yang-Mills theory with fermions and vector fields. The particular representation of the vector fields permits to formulate diffeomorphism invariant kinetic terms. Geometry and general relativity emerge at large distances by spontaneous symmetry breaking inducing masses for the gauge bosons. We propose here a model of pregeometry for which the difference between time and space, as reflected by the signature of the metric, arises from spontaneous symmetry breaking of the local SO(4,,$mathbb{C}$)-gauge symmetry. For a euclidean metric all fields have a standard propagator at high momenta. Analytic continuation to a Minkowski-metric is achieved by a change of field values. We conjecture that a quantum effective action of this type is consistent with unitarity and well behaved in the short distance limit.
We investigate Euclidean wormholes in Gauss-Bonnet-dilaton gravity to explain the creation of the universe from nothing. We considered two types of dilaton couplings (i.e., the string-inspired model and the Gaussian model) and we obtained qualitatively similar results. There can exist Euclidean wormholes that explain the possible origin of our universe, where the dilaton field is located over the barrier of dilaton potential. This solution can exist even if dilaton potential does not satisfy slow-roll conditions. In addition, the probability is higher than that of the Hawking-Moss instanton with the same final condition. Therefore, Euclidean wormholes in Gauss-Bonnet-dilaton gravity are a possible and probable scenario, which explains the origin of our universe.
By making use of the background field method, the one-loop quantization for Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is investigated. Using generalized zeta function regularization, the on-shell and off-shell one-loop effective actions are explicitly obtained and one-loop renormalizability, as well as the corresponding one-loop renormalization group equations, are discussed. The so called critical gravity is also considered.
We consider the question of whether consistency arguments based on measurement theory show that the gravitational field must be quantized. Motivated by the argument of Eppley and Hannah, we apply a DeWitt-type measurement analysis to a coupled system that consists of a gravitational wave interacting with a mass cube. We also review the arguments of Eppley and Hannah and of DeWitt, and investigate a second model in which a gravitational wave interacts with a quantized scalar field. We argue that one cannot conclude from the existing gedanken experiments that gravity has to be quantized. Despite the many physical arguments which speak in favor of a quantum theory of gravity, it appears that the justification for such a theory must be based on empirical tests and does not follow from logical arguments alone.
We show that if one starts with a Universe with some matter and a cosmological constant, then quantum mechanics naturally induces an attractive gravitational potential and an effective Newtons coupling. Thus gravity is an emergent phenomenon and what should be quantized are the fundamental degrees of freedom from which it emerges.
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