The cosmological constant and Pioneer anomaly from Weyl spacetimes and Mach's principle

Carlos Castro
2009 Physics Letters B  
It is shown how Weyl's geometry and Mach's Holographic principle furnishes both the magnitude and sign (towards the sun) of the Pioneer anomalous acceleration aP ∼ −c 2 /R Hubble firstly observed by Anderson et al. Weyl's Geometry 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
more » ... ns. A nonvanishing value of the vacuum energy density of the order of 10 −123 M 4 P lanck is found consistent with observations. Weyl's geometry accounts also for the phantom scalar field in modern Cosmology in a very natural fashion. The problem of dark energy is one of the most challenging problems facing Cosmology today with a vast numerable proposals for its solution, we refer to the recent monograph [1], [3] and references therein. In [4] we have shown how Weyl's geometry (and its scaling symmetry) is instrumental to solve this dark energy riddle. In this letter we will show how Weyl's geometry in an elegant fashion can account for both the magnitude and sign of the Pioneer anomalous acceleration [5] . Before starting we must emphasize that our procedure [4] was quite different than previous proposals [2] to explain dark matter ( instead of dark energy ) in terms of Brans-Dicke gravity. It is not only necessary to include the Jordan-Brans-Dicke scalar field φ but it is essential to have a Weyl geometric extension and generalization of Riemannian geometry ( ordinary gravity ). Weyl's geometry main feature is that the norm of vectors under parallel infinitesimal displacement going from x µ to x µ + dx µ change as follows
doi:10.1016/j.physletb.2009.03.079 fatcat:zkbsq6ruezbxzf3udcylc22gd4