Cheng–Weyl vector field and its cosmological application

Abstract

Weyl’s idea on scale invariance was resurrected by Cheng in 1988. The requirement of localscale invariance leads to a completely new vector field, which we call the ‘Cheng–Weylvector field’. The Cheng–Weyl vector field couples only to a scalar field and thegravitational field naturally. It does not interact with other known matter in the standardmodel of particle physics. In the present work, the (generalized) Cheng–Weyl vector fieldcoupled with the scalar field and its cosmological application are investigated. A mixture ofthe scalar field and a so-called ‘cosmic triad’ of three mutually orthogonal Cheng–Weylvector fields is regarded as the dark energy in the universe. The cosmologicalevolution of this ‘mixed’ dark energy model is studied. We find that the effectiveequation-of-state parameter of the dark energy can cross the phantom dividewde = −1 in some cases; the first and second cosmological coincidence problems can be alleviated atthe same time in this model.