Cheng–Weyl vector field and its cosmological application

Weyl's antiquated idea of scale invariance was resurrected by Cheng in 1988, almost 60 years later. The requirement of local scale invariance leads to the existence of a completely new vector field, which we call as ``Cheng-Weyl vector field''. The Cheng-Weyl vector field only couples to the scalar field and the gravitational field naturally. It does not interact with other known matters in the particle physics standard model. In the present work, the (generalized) Cheng-Weyl vector field coupling with a scalar field and its cosmological application are investigated. We regard the dark energy as a mixture of a scalar field and a so-called ``cosmic triad'' of three mutually orthogonal Cheng-Weyl vector fields. The cosmological evolution of this ``mixed'' dark energy is studied. We find that the effective equation-of-state parameter of dark energy can cross the phantom divide wde=-1 in some cases; the first and second cosmological coincidence problems can be alleviated at the same time in this model.