The generalized Brans-Dicke theory and its cosmology

Abstract

A generalized Brans-Dicke (GBD) theory is studied in this paper. The GBD theory is obtained by generalizing the Ricci scalar R to an arbitrary function f (R) in the original Brans-Dicke (BD) action.The interesting property has been found in the GBD theory, for example it can naturally solve the problem of γ value emerging in f (R) modified gravity (i.e. the inconsistent problem between the observational γ value and the theoretical γ value), without introducing the so-called chameleon mechanism. In this paper, we derive the cosmological equations and study the cosmology in the GBD theory. The cosmological solutions show that the GBD model can pass through the test of the observations, such as the observational Hubble data. Comparing with other theories, it can be found that the GBD theory have some other interesting properties or solve some problems existing in other theories. (1) It is well known that the f (R) theory are equivalent to the BD theory with a potential (abbreviated as BDV) for taking a specific value of the BD parameter ω = 0, where the specific choice: ω = 0 for the BD parameter is quite exceptional, and it is hard to understand the corresponding absence of the kinetic term for the field. However, for the GBD theory, it is similar to the double scalar-fields model, and both fields in the GBD own the non-disappeared dynamical effect.(2) One knows that in the double scalar-fields quintom model, it is required to include both the canonical quintessence field and the non-canonical phantom field in order to make the state parameter to cross over w = −1, while several fundamental problems are associated with phantom field, such as the problem of negative kinetic term and the fine-tuning problem, etc. While, in the GBD model, the state parameter of geometrical dark energy can cross over the phantom boundary w = −1 as achieved in the quintom model, without bearing the problems existing in the quintom model. (3) The GBD theory tends to investigate the physics from the viewpoint of geometry, while the BDV or the two scalar-fields quintom model tends to solve physical problems from the viewpoint of matter. It is possible that several special characteristics of scalar fields could be revealed through studies of geometrical gravity in the GBD. As an example, we investigate the potential V (φ) of the BD scalar field, and an effective form of V (φ) could be given by studying on the GBD theory. And, it seems that a viable condition for the BD theory could be found, i.e. the BD parameter should be ω > 0 for f > 0, if we assume that the effective form of the BD potential can be approximately written as a popular square function of φ.

Çok Tabakalı Evren Modeli Üzerine Genel Bakış

“…Çünkü bu çalışmalar neticesi sağlanabilecek yeni açılımlar; günümüz teknolojisinin ilerlemesine büyük katkılar sağlayabilme potansiyeline sahiptir. Literatürde evreni daha çok açıklamayı amaçlayan çalışmaların bazıları şunlardır: Evreni açıklamak için Lu ve arkadaşları [4], Bhattachrya ve arkadaşları [5] Brans-Dicke teorisi üzerine araştırmalar yapmışlardır. Yine evreni açıklamak amacıyla Kao [6] Scalar-Tensor teorisi üzerine, Dijkgraaf ve arkadaşları [7] String teorisi üzerine çalışmışlar yapmışlardır.…”

Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory

“…Recently, a different strategy was proposed to modify the BD theory (called GBD) in Refs. [50,51] by generalizing the Ricci scalar R to be an arbitrary function f (R) in the BD action. Comparing with other modified theories, one can find that the GBD theory in the metric formalism have some interesting properties or solve some problems existing in other theories [50,51].…”

“…[50,51] by generalizing the Ricci scalar R to be an arbitrary function f (R) in the BD action. Comparing with other modified theories, one can find that the GBD theory in the metric formalism have some interesting properties or solve some problems existing in other theories [50,51]. Several results could be exhibited briefly as follows.…”

“…Several results could be exhibited briefly as follows. (1) The state parameter of geometrical dark energy in the GBD model can cross over the phantom boundary w = −1 as achieved in the quintom model, without bearing the problems existing in the quintom model [51] (in the double scalar-fields quintom model, it is required to include both the canonical quintessence field and the non-canonical phantom field in order to make the state parameter to cross over w = −1 [52,53], while several fundamental problems are associated with phantom field, such as the problem of negative kinetic term and the fine-tuning problem, etc). ( 2) One knows that the metric-formalism f (R) theories are equivalent to the BD theory with a potential (abbreviated as BDV) for taking a specific value of the coupling parameter ω = 0 [18], where the specific choice: ω = 0 is quite exceptional, and it is hard to understand the corresponding absence of the kinetic-energy term for the field in the action.…”

“…( 2) One knows that the metric-formalism f (R) theories are equivalent to the BD theory with a potential (abbreviated as BDV) for taking a specific value of the coupling parameter ω = 0 [18], where the specific choice: ω = 0 is quite exceptional, and it is hard to understand the corresponding absence of the kinetic-energy term for the field in the action. However, the BD field in the GBD theory owns the non-disappeared kinetic term in the action [50,51]. (3) Using the method of the weak-field approximation Ref.…”