Scalar–vector–tensor gravity from preferred reference frame effects

Abstract

Using some suitable combinations of a dynamical unit time-like fourvelocity 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 spacetime. 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 ω 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.

Galaxy rotation curves and preferred reference frame effects

“…In both of them the space-time coordinates are still real coordinates. Whereas an ordinary way to obtain an Euclidean metric solution of the Einstein field equations, is to introduce a complex time variable τ = it, so the Lorentzian signature of the metric is changed to its Euclidean version [22]. In accordance with the works has been done previously [4,7,8,9,10], in the weak field approximation the potential for a matter distribution of an extended object behaves like the Newtonian potential with an enhanced gravitational constant and an additional Yukawa potential.…”

“…Another approach was used to extend the Jordan-Brans-Dicke scalar-tensor gravity theory [21] and called as Jordan-Brans-Dicke scalar-vector-tensor (JBD-SVT) model by one of the authors in refs. [22,23]. Several applications of this model are studied in refs.…”

“…One of the remarkable results of a suitable dynamical preferred frame, is to have two metrics with inequivalent causal structure named as Lorentzian and Euclidean metrics, respectively. The quantum cosmology viewpoint of the very early universe models describe its origin as a quantum tunneling from Euclidian to the Lorentzian space-time [22]. In both of them the space-time coordinates are still real coordinates.…”

“…In accordance with the works has been done previously [4,7,8,9,10], in the weak field approximation the potential for a matter distribution of an extended object behaves like the Newtonian potential with an enhanced gravitational constant and an additional Yukawa potential. Applying a general potential U(φ, N µ ) and weak field approximation of the background metric obtained from dynamical field equations of the JBD-SVT gravity model [22] we study rotation curves of galaxies without postulating exotic dark matter which usually is described by dynamical scalar fields. This paper is organized as follows: In section 2 we defined the JBD-SVT gravity [22] and calculate weak field limit of the Lagrangian density of the model for spherically symmetric state metric equation.…”

“…Applying a general potential U(φ, N µ ) and weak field approximation of the background metric obtained from dynamical field equations of the JBD-SVT gravity model [22] we study rotation curves of galaxies without postulating exotic dark matter which usually is described by dynamical scalar fields. This paper is organized as follows: In section 2 we defined the JBD-SVT gravity [22] and calculate weak field limit of the Lagrangian density of the model for spherically symmetric state metric equation. Then we obtained linear order solutions of the Euler-Lagrange equations of the fields.…”