A Weyl-Dirac cosmological model with DM and DE

Abstract

In the Weyl-Dirac (W-D) framework a spatially closed cosmological model is considered. It is assumed that the space-time of the universe has a chaotic Weylian microstructure but is described on a large scale by Riemannian geometry. Locally fields of the Weyl connection vector act as creators of massive bosons having spin 1. It is suggested that these bosons, called weylons, provide most of the dark matter in the universe. At the beginning the universe is a spherically symmetric geometric entity without matter. Primary matter is created by Dirac's gauge function very close to the beginning. In the early epoch, when the temperature of the universe achieves its maximum, chaotically oriented Weyl vector fields being localized in micro-cells create weylons. In the dust dominated period Dirac's gauge function is giving rise to dark energy, the latter causing the cosmic acceleration at present. This oscillatory universe has an initial radius identical to the Plank length = 1.616 exp (-33) cm, at present the cosmic scale factor is 3.21 exp (28) cm, while its maximum value is 8.54 exp (28) cm. All forms of matter are created by geometrically based functions of the W-D theory.

The conformal transformation’s controversy: what are we missing?

“…For readable and pedagogical introduction to WG we recommend the classical books [22], [23], and [24], however research papers can be found where the subject is exposed in a more or less pedagogical way [25][26][27][28]. It has to be said that, although there was a moderate revival of Weyl's ideas after Dirac's "large numbers hypothesis" [29] (see also [30]), in the last decades there has been a renewed interest in WG [27,28,[31][32][33][34][35][36][37], in connection to the search for alternative explanations to outstanding questions of fundamental physics, such as the dark matter/dark energy issues. A Weyl space (M, g µν , w µ ), is a manifold M endowed with a metric g µν and a (gauge) vector field w µ , so that the following "metricity" condition is satisfied:…”

“…This is to be contrasted with vacuum BD theory where this is a mirage or spurious symmetry instead. Put in different words: in the gravitational theory depicted by (35), (36), the laws of gravity look the same in the different conformal frames, while the spacetime coincidences -properly the observations -are unchanged. This is an outstanding example of a theory where, unlike BD theory, the different conformal descriptions of a given phenomenon are actually (physically and mathematically) equivalent.…”

“…After the analysis in section V, it is almost trivial to show that the scale-invariant theory of gravity given by (35), (36), is free of the positivity of energy problem, including fulfillment of the energy conditions. In fact, the first thing to notice is that, in the action (35), the kinetic energy term of the gauge field ϕ is absent.…”

“…There are several mathematical consequences arising from assuming WI spaces as the natural geometrical basis for a scale-invariant theory of gravity (35), (36). In particular, due to invariance under (15), the metric g µν and the gauge scalar ϕ are far from unique.…”

The Weyl–Cartan Gauss–Bonnet gravity

“…This implies that one has the freedom to choose the unit length at each point, which is the Weyl gauge freedom [1]. A variety of works have been done in the Weyl geometry including the cosmology [2], relations to scalar-tensor [3] and teleparallel theories [4]. One can also restrict the form of Weyl vector to be a derivative of a scalar as w µ = ∂ µ φ [5].…”