Relativity and Cosmology


On Dark Energy, Weyl Geometry and Brans-Dicke-Jordan Scalar Field

Authors: Carlos Castro

We review firstly why Weyl's Geometry, within the context of Friedman-Lemaitre-Robertson-Walker cosmological models, can account for both the origins and the value of the observed vacuum energy density (dark energy). The source of dark energy is just the dilaton-like Jordan-Brans-Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. A nonvanishing value of the vacuum energy density of the order of 10-123M4Planck is derived in agreement with the experimental observations. Next, a Jordan-Brans-Dicke gravity model within the context of ordinary Riemannian geometry, yields also the observed vacuum energy density (cosmological constant) to very high precision. One finds that the temporal flow of the scalar field φ(t) in ordinary Riemannian geometry, from t = 0 to t = to, has the same numerical effects (as far as the vacuum energy density is concerned) as if there were Weyl scalings from the field configuration φ(t), to the constant field configuration φo, in Weyl geometry. Hence, Weyl scalings in Weyl geometry can recapture the flow of time which is consistent with Segal's Conformal Cosmology, in such a fashion that an expanding universe may be visualized as Weyl scalings of a static universe. The main novel result of this work is that one is able to reproduce the observed vacuum energy density to such a degree of precision 10-123M4Planck, while still having a Big-Bang singularity at t = 0 when the vacuum energy density blows up. This temporal flow of the vacuum energy density, from very high values in the past, to very small values today, is not a numerical coincidence but is the signal of an underlying Weyl geometry (conformal invariance) operating in cosmology, combined with the dynamics of a Brans-Dicke-Jordan scalar field.

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Submission history

[v1] 3 Jan 2009

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