Cheng-Weyl vector field and its cosmological application

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