Pregeometry and euclidean quantum gravity

Abstract

Einstein's 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. 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.

Reconstructing the graviton

“…Similar properties may be present in AS quantum gravity. For a first discussion see [31], for related recent work see [32][33][34]. In the present work, we formally show that the spectral function of the background graviton has non-positive parts.…”

“…The prefactor only decays with 1/p 2 for p → ∞. This entails that for η ḡ < 0, the spectral integral in (33) has to decay at least as pηḡ/2 in order to be compatible with (28) for the background propagator. This leads us to…”

Pregeometry and spontaneous time-space asymmetry

“…A discussion of euclidean quantum gravity for the gauge group SO (4) and real e m µ can be found in ref. [44]. Our setting will be more general and involve additional degrees of freedom.…”