Nowadays cosmology with the Weyl-Dirac approach
  Some problems of cosmology: the big bang singularity, the origin of conventional matter, of dark matter and of dark energy may be successfully described and treated in the framework of the Weyl-Dirac theory. This theory, being a minimal expansion of Einstein's GRT, contains in addition to the metric tensor\g, the Weyl connection vector \w and the Dirac gauge function\beta. From these geometrically based quantities one obtains the behavior of our universe. The Weyl connection vector \w existing in microcells creates dark matter particles, weylons. In the very early universe \beta creates matter, whereas in the present dust period \beta forms dark energy, the latter causing cosmic acceleration. Around a massive body the - dark energy form a ball-like concentration having negative mass and negative pressure. These \beta-balls cause an additional acceleration of the expanding universe. The Weyl-Dirac theory is a classical geometrically based framework appropriate for describing and searching cosmology. 
Mark Israelit
gr-qc astro-ph.CO