WEYL-DIRAC QUINTESSENCE AND DARK MATTER

In the Integrable Weyl-Dirac theory we consider a spatially closed universe undergoing at present accelerated expansion, having a non-vanishing cosmological constant, and filled with luminous- and dark matter. During the dust-dominated period, dark matter and the quintessence pressure, the latter giving rise to acceleration: both are created by the Dirac gauge function. The behavior of F-R-W models is considered in appropriate gauges, and plausible scenarios are obtained. The outcome of the present paper, together with results of a previous work, provide a geometrically based, classical, singularity-free model of the universe. This has originated from a pure geometric Weyl-Dirac entity, passed a prematter period, the radiation-dominated era, and continues its development in the present dust period.

COVARIANT CONFORMAL DECOMPOSITION OF EINSTEIN EQUATIONS

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-"metric" (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this "metric", of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.