Scalar–vector–tensor gravity from preferred reference frame effects

Abstract

Using some suitable combinations of a dynamical unit time-like four-velocity of a preferred reference frame, Ricci tensor and covariant derivatives of the Brans–Dicke (BD) scalar field, we propose a new scalar–vector–tensor gravity model in which an Euclidean Jordan–Brans–Dicke (JBD) action is reduced to its Lorentzian version with no used complex coordinates. Thus it should be play an important role in the process of metric signature transition of a suitable dynamical curved space-time. In this work we follow the ideas proposed by Barbero et al. As an application of the model, we study a classical perfect fluid cosmological universe described in a flat Robertson–Walker background metric. Mathematical derivations of the equations predict a non-singular scale factor for the space-time in the both of dust and radiation dominated states where value of the Brans–Dicke parameter \({\omega}\) is fixed, but there is still an arbitrary parameter which should be determined by the boundary values of the cosmological system. Furthermore its classical cosmological vacuum solutions is obtained as a non-singular model with a fixed Brans–Dicke parameter. Although there is obtained a singular perfect fluid cosmological solution which may not be suitable, because in this case the Brans–Dicke parameter is not still fixed.