In this paper, we study some relevant cosmological features of a Dark Energy (DE) model with Granda-Oliveiros cut-off, which is just a specific case of Nojiri-Odintsov holographic DE unifying phantom inflation with late-time acceleration, in the framework of Chameleon Brans-Dicke (BD) Cosmology. Choosing a particular ansatz for some of the quantities involved, we derive the expressions of some important cosmological quantities, like the Equation of State (EoS) parameter of DE $w_D$, the effective EoS parameter $w_{eff}$, the pressure of DE $p_D$ and the deceleration parameter $q$. Moreover, we study the behavior of statefinder parameters $r$ and $s$, of the cosmographic parameters $j$, $s_{cosmo}$, $l$ and $m$ and of the squared speed of the sound $v_s^2$ for both case corresponding to non interacting and interacting Dark Sectors. We also plot the quantities we have derived and we calculate their values for $t\rightarrow 0$ (i.e. for the beginning of the Universe history), for $t\rightarrow \infty$ (i.e. for far future) and for the present time, indicated with $t_0$. The EoS parameters have been tested against various observational values available in the literature.
We investigate the dynamics of the chameleonic Generalised Brans--Dicke model in flat FRW cosmology. In a new approach, a framework to study stability and attractor solutions in the phase space is developed for the model by simultaneously best fitting the stability and model parameters with the observational data. The results show that for an accelerating universe the phantom crossing does not occur in the past and near future.
In the present work we have studied some features of the generalized Brans-Dicke (BD) model in which the scalar field is allowed to couple non-minimally with matter sector. Extended holographic Ricci dark energy (EHRDE) has been considered in the above framework of BD cosmology. Some restrictions have been derived for the BD parameter $ω$ and a stronger matter-chameleon coupling has been observed with expansion of the universe. In this framework, the equation of state parameter of EHRDE has behaved like quintom. Also, we have reconstructed the potential and coupling function for BD model for t…
Motivated by the work of Yang et al., \emph{Mod. Phys. Lett. A}, \textbf{26}, 191 (2011), we report a study on the New Holographic Dark Energy (NHDE) model with energy density given by $ρ_D=\frac{3ϕ^2}{4ω}(μH^2+ν\dot{H})$ in the framework of chameleon Brans-Dicke cosmology. We have studied a correspondence between the quintessence, the DBI-essence and the tachyon scalar field models with the NHDE model in the framework of chameleon Brans-Dicke cosmology. Deriving an expression of the Hubble parameter $H$ and, accordingly, $ρ_D$ in the context of chameleon Brans-Dicke chameleon cosmology, we ha…
We consider a generalized Brans-Dicke model in which the scalar field has a potential function and is also allowed to couple non-minimally with the matter sector. This anomalous gravitational coupling can in principle avoid the model to pass local gravity experiments. One then usually assumes that the scalar field has a chameleon behavior in the sense that it acquires a density-dependent effective mass. While it can take a small effective mass in cosmological (low-density environment) scale, it has a sufficiently heavy mass in Solar System (large-density environment) and then hides gravity tes…
The authors of Ref. \cite{1-2}, investigated cosmic evolution in an external interacting model of scalar tensor gravity namely Brans Dicke chameleon scenario. The procedure of this work contains novelties but, it shall be observed from this comment, their report faces three fundamental drawbacks. One of them concerns the energy conservation equation, and the other two flaws are about mathematical mistakes. In the scalar tensor gravity models, a well-known method, in order to obtain conservation equation one must combine Friedmann equations with modified Klein-Gordon equation. But in Ref. \cite…
Based on \cite{16}, we assume there is a non-minimal coupling between the scalar field and matter in Brans-Dicke model. We analyzes the motion of different matter such as, massless scalar field, photon, massless perfect fluid (dust), massive perfect fluid and point particle matter in this theory. We show that the motion of massless scalar field and photon can satisfy null geodesic motion only in high frequency limit. Also we find that the motion of the dust and massive perfect fluid is geodesic for $L_m=-P$ and is non-geodesic for $L_m=\R$. Finally, we study the motion of point particle and sh…
In this paper we consider Chameleonic Generalized Brans--Dicke Cosmology in the framework of FRW universes. The bouncing solution and phantom crossing is investigated for the model. Two independent cosmological tests: Cosmological Redshift Drift (CRD) and distance modulus are applied to test the model with the observation.
We consider the Post-Newtonian limit of massive Brans-Dicke theory and we make some notes about the Post-Newtonian limit of the case $ω=0$. This case is dynamically equivalent to the metric $f(R)$ theory. It is known that this theory can be compatible with the solar system tests if Chameleon mechanism occurs. Also, it is known that this mechanism is because of the non-linearity in the field equations produced by the largeness of the local curvature relative to the background curvature. Thus, the linearization of the field equations breaks down. On the other hand we know that Chameleon mechanis…
In this paper it is shown that in Brans - Dicke theory, if one considers a non-minimal coupling between the matter and the scalar field, it can give rise to a late time accelerated expansion for the universe preceded by a decelerated expansion for very high values of the Brans - Dicke parameter $ω$.
We investigate chameleonic Brans--Dicke model applied to the FRW universes. A framework to study stability and attractor solutions in the phase space is developed for the model. We show that depending on the matter field and stability conditions, it is possible to realize phantom-like behavior without introducing phantom filed in the model while the stability is fulfilled and phantom crossing occurs. The statefinder parameters to the model for different kinds of matter interacting with the chameleon scalar field are studied. We also compare our model with present day observations.
The post Newtonian parameter is considered in the Chameleon-Brans-Dicke frame. In the first step, the general form of this parameter and also effective gravitational constant is obtained. An arbitrary function for $f(Φ)$, which indicates the coupling between matter and scalar field, is introduced to investigate validity of solar system constraint. It is shown that Chameleon-Brans-Dicke model can satisfy the solar system constraint and gives us an $ω$ parameter of order $10^4$, which is in comparable to the constraint which has been indicated in {\cite{17-a}}.
We consider a generalized Brans-Dicke model in which the scalar field has a potential function and is also allowed to couple non-minimally with the matter sector. We assume a power law form for the potential and the coupling functions as the inputs of the model and show that acceleration of the universe can be realized for a constrained range of exponent of the potential function. We also argue that this accelerating phase is consistent with a large and positive Brans-Dicke parameter. In our analysis, the potential plays a more important role with respect to the coupling function in dynamics o…
We study a cosmological implication of holographic dark energy in the Brans-Dicke gravity. We employ the holographic model of dark energy to obtain the equation of state for the holographic energy density in non-flat (closed) universe enclosed by the event horizon measured from the sphere of horizon named $L$. Our analysis shows that one can obtain the phantom crossing scenario if the model parameter $α$ (of order unity) is tuned accordingly. Moreover, this behavior is achieved by treating the Brans-Dicke scalar field as a Chameleon scalar field and taking a non-minimal coupling of the scalar …
Motivated by the recent work of one of us [1], we generalize this work to the case where the pressureless dark matter and the holographic dark energy do not conserve separately but interact with each other. We investigate the cosmological applications of interacting holographic dark energy in Brans-Dicke theory with chameleon scalar field which is non-minimally coupled to the matter field. We find out that in this model the phantom crossing can be constructed if the model parameters are chosen suitably. We also perform the study for the new agegraphic dark energy model and calculate some relev…
We study the holographic dark energy (HDE) model in generalized Brans-Dicke scenario with a non-minimal coupling between the scalar field and matter lagrangian namely Chameleon Brans Dicke (CBD) mechanism. In this study we consider the interacting and non-interacting cases for two different cutoffs. The physical quantities of the model such as, equation of state (EoS) parameter, deceleration parameter and the evolution equation of dimensionless parameter of dark energy are obtained. We shall show that this model can describe the dynamical evolution of fraction parameter of dark energy in all e…
In this paper we investigate the chameleon effect in the different conformal frames of the Brans--Dicke theory. Given that, in the standard literature on the subject, the chameleon is described in the Einstein frame almost exclusively, here we pay special attention to the description of this effect in the Jordan and in the string frames. It is shown that, in general, terrestrial and solar system bounds on the mass of the BD scalar field, and bounds of cosmological origin, are difficult to reconcile at once through a single chameleon potential. We point out that, in a cosmological context, prov…
We study the stability of the ghost dark energy model versus perturbation. Since this kind of dark energy is instable in Einsteinian general relativity theory, then we study a new type of Brans-Dicke theory which has non-minimal coupling with matter which is called chameleon Brans-Dicke (CBD) model of gravity. Due to this coupling the equation of conservation energy is modified. For considering the stability of the model we use the adiabatic squared sound speed, $c_s^2$, whose sign of it determines the stability of the model in which for $c_s^2 >0 $ the model is stable and for $c_s^2 <0 $ the …
We have investigated a brane world model in which the gravitational field in the bulk is described both by a metric tensor and a minimally coupled scalar field. This scalar field is taken to be a chameleon with an appropriate potential function. The scalar field interacts with matter and there is an energy transfer between the two components. We find a late-time asymptotic solution which exhibits late-time accelerating expansion. We also show that the Universe recently crosses the phantom barrier without recourse to any exotic matter. We provide some thermodynamic arguments which constrain bot…
We analyse modelling techniques for the large-scale structure formed in scalar-tensor theories of constant Brans-Dicke parameter which match the concordance model background expansion history and produce a chameleon suppression of the gravitational modification in high-density regions. Thereby, we use a mass and environment dependent chameleon spherical collapse model, the Sheth-Tormen halo mass function and linear halo bias, the Navarro-Frenk-White halo density profile, and the halo model. Furthermore, using the spherical collapse model, we extrapolate a chameleon mass-concentration scaling r…
We consider a Brans-Dicke cosmology in five-dimensional space-time. Neglecting the quadratic and the mixed Brans-Dicke terms in the Einstein equation, we derive a modified wave equation of the Brans-Dicke field. We show that, at high energy limit, the 3-brane Brans-Dicke cosmology could be described as the standard one by changing the equation of state. Finally as an illustration of the purpose, we show that the dark energy component of the universe agrees with the observations data.
We present the new interpretation of scalar field for the Brans-Dicke theory. This interpretation is obtained by considering a fixed spacetime structure of manifold.
We study the Generalized Brans-Dicke cosmology in the presence of matter and dark energy. Of particular interest for a constant Brans-Dicke parameter, the de Sitter space has also been investigated.
In this short letter we present a some rigorous vacuum solutions of the D-dimensional Jordan-Brans-Dicke field equations. In contrast with the well known Brans-Dicke solutions, to the search of static and spherically symmetric space-time we choose the widespread Hilbert coordinates.
We present the static spherically symmetric vacuum solutions of the Jordan, Brans-Dicke field equations. The new solutions are obtained by considering a polar Gaussian, isothermal and radial hyperbolic metrics.
We consider Brans-Dicke theory with a self-interacting potential in Einstein conformal frame. We show that an accelerating expansion is possible in a spatially flat universe for large values of the Brans-Dicke parameter consistent with local gravity experiments.
We study spherically symmetric solutions to the Jordan-Brans-Dicke field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. Assuming a perfect fluid with the equation of state, we show that there are static interior nontrivial solutions in three dimensional Jordan-Brans-Dicke gravity theory.
We discuss the physical equivalence between the Einstein and Jordan frames in Brans-Dicke theory. The inequivalence of conformal transformed theories is clarified with the help of an old equivalence theorem of Chrisholm's.
It is shown that the recently claimed two new Brans-Dicke wormhole solutions [F. He and S-W. Kim, Phys. Rev. D{\bf 65}, 084022 (2002)] are not really new solutions. They are just the well known Brans-Dicke solutions of Class I and II in a different conformal gauge.
We have studied the properties of the static, spherically symmetric solution of Jordan, Brans-Dicke theory. An exact interior solution for standard space-time line element in the Schwarzschild form is obtained.
A simple Lorentzian vacuum wormhole solution of Brans-Dicke gravitation is presented and analysed. It is shown that such solution holds for both, the Brans-Dicke theory endowed with torsion (for a value of the coupling parameter $ω> 1/2$) and for the vacuum -no torsion- case (for $ω< -2$).
A simple Heckmann's vacuum wormhole solution of Jordan-Brans-Dicke gravitation is presented and analysed. It is shown that in contrast with class I Brans solution where the throat radius becomes real when $ω< -4/3$ here it becomes positive when $ω< -1$.
We present static cylindrically symmetric electrovac solutions in the framework of the Brans-Dicke theory and show that our solution yields some of the well-known solutions for special values of the parameters of the resulting metric functions.
A two-way traversable wormhole solution in Brans-Dicke theory with torsion is obtained using the method of massive thin shells. The solution goes over general relativity for an infinite large value of the coupling parameter, however, the Brans-Dicke scalar could never be the ``carrier'' of exoticity that threads the wormhole throat.
We discuss the correspondence between metric $f(R)$ gravity and $ω=0$ Brans-Dicke theory with a potential, by working out an example that reconfirms this equivalence.
Spherically symmetric thin-shell wormholes are constructed within the framework of Brans-Dicke gravity. It is shown that, for appropriate values of the Brans-Dicke constant, these wormholes can be supported by matter satisfying the energy conditions.
The $ω\to\infty$ limit of Brans-Dicke theory is studied with the help of the conformal transformation approach without resorting, however, to the conformal invariance property of this formalism, that is shown to be spurious.
This paper is devoted to study the accelerated expansion of the universe by exploring the Brans-Dicke parameter in different eras. For this purpose, we take FRW universe model with viscous fluid (without potential) and Bianchi type I universe model with barotropic fluid (with and without potential). We evaluate deceleration parameter as well as Brans-Dicke parameter to explore cosmic acceleration. It is concluded that accelerated expansion of the universe can also be achieved for higher values of the Brans-Dicke parameter in some cases.
We analyse the fate of density perturbation in the Brans-Dicke Theory, giving a general classification of the solutions of the perturbed equations when the scale factor of the background evolves as a power law. We study with details the cases of vacuum, inflation, radiation and incoherent matter. We find, for the a negative Brans-Dicke parameter, a significant amplification of perturbations.
The definition of the Sparling-Thirring form is extended to the Brans-Dicke theory. By writing the Brans-Dicke field equations in a formally Maxwell-like form, a superpotential and a corresponding pseudo energy-momentum form are defined. The general energy expression provided by the superpotential in the Jordan frame is discussed in relation to the corresponding expression in the Einstein frame. In order to substantiate its formal definition, the generalized Sparling-Thirring form is used to calculate the energy for the spherically symmetric vacuum solution in the Brans-Dicke theory.
The Brans-Dicke Theory of Gravity is one of the most promising alternatives to the Einstein's Theory of General Relativity. We have examined an action term with wrong signs for both the kinetic and mass terms for the scalar field and have found solutions for both the scale factor of the universe and the Brans-Dicke scalar field which vary exponentially in time.
Analytical wormhole solutions in Brans-Dicke theory in the presence of matter are presented. It is shown that the wormhole throat must not be necessarily threaded with exotic matter.
The gravitational fields of vacuumless global and gauge strings have been studied in Brans-Dicke theory under the weak field assumption of the field equations. It has been shown that both global and gauge string can have repulsive as well as attractive gravitational effect in Brans-Dicke theory which is not so in General Relativity.
We consider the embedding of 3+1 dimensional cosmology in 4+1 dimensional Jordan-Brans-Dicke theory. We show that exponentially growing and power law scale factors are implied. Whereas the 4+1 dimensional scalar field is approximately constant for each, the effective 3+1 dimensional scalar field is constant for exponentially growing scale factor and time dependent for power law scale factor.
In order to investigate more features of the Brans-Dicke cosmology in the five-dimensional space-time, we explore the solutions of its dynamiacal systems. A behavior of the universe in its early and late time by means of the scale factor is considered. As a results, we show that it is possible to avoid the big rip singularity and to cross the phantom divide line. Furthermore, we review the dark energy component of the universe and its agreement with the observation data for this 3-brane Brans Dicke cosmology by means of the cosmological parameters.
It is known that Vilenkin's phenomenological equation of state for static straight cosmic strings is inconsistent with Brans-Dicke theory. We will prove that, in the presence of a cosmological constant, this equation of state is consistent with Brans-Dicke theory. The general solution of the full nonlinear field equations, representing the interior of a cosmic string with a cosmological constant is also presented.
A `no-hair' theorem for the Brans-Dicke field, in the domain of outer communications of a static black hole, is established, when the trace of the energy-momentum tensor, T, is a definite-sign scalar. This implies that Brans-Dicke theory of gravitation, for matter with T of definite sign, is equivalent to Einstein gravity with the constraint T=0.
The Geodesic Deviation Equation is being studied in Brans-Dicke-Rastall gravity. We briefly discuss the Brans-Dicke-Rastall gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the Brans-Dicke-Rastall gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector $η(z)$ and observer area distance $r_0(z)$ and compare the results with $Λ$CDM model.
We present a new exact solution in Brans-Dicke theory. The solution describes inhomogeneous plane-symmetric perfect fluid cosmological model with an equation of state $p=γρ$. Some main properties of the solution are discussed.
The spectra of relic gravitational waves produced as a result of cosmological expansion of the inflationary models are derived in Brans-Dicke theory of gravity.The time dependence of the very early Hubble parameter and matter energy density are derived from frequency dependent spectrum of relic gravitational waves.Also it is found that Brans-Dicke scalar field contributes to the energy density of relic gravitons.
We have solved cosmological gravitational Wave(GW)equation in the frame work of Generalised Brans-Dicke(GBD) theory for all epochs of the Universe.The solutions are expressed in terms of the present value of the Brans-Dicke coupling parameter $ω(ϕ)$.It is seen that the solutions represent travelling growing modes for negative values of $ω_{0}$ for all epochs of the Universe.
A gravitating global monopole produces a repulsive grativational field outside the core in addition to a solid angular deficit in the Brans-Dicke theory. As a new feature, the angular deficit is dependent on the values of ϕ_{\infty} and ω, where ϕ_{\infty} is asymptotic value of scalar field in space-like infinity and ωis the Brans-Dicke parameter.
We derive the full projected Einstein-Brans-Dicke gravitational equations associated with a n-dimensional brane embedded in a (n+1)-dimensional bulk. By making use of general conditions, as the positivity of the Brans-Dicke parameter and the effective Newton gravitational constant as well, we are able to constrain the brane cosmological constant in terms of the brane tension, the Brans-Dicke scalar field, and the trace of the stress tensor on the brane, in order to achieve a $dS$ brane. Applying these constraints to a specific five-dimensional model, a lower bound for the scalar field on the b…
This article examines the claim that the Brans-Dicke scalar field ϕ\to ϕ_{0} + O(1/\sqrtω) for large $ω$ when the matter field is traceless. It is argued that such a claim can not be true in general.
We show that Gravitational Waves are exponetially amplified in the inflationary phase in Brans-Dicke theory, so that it would be possible to detect them and in this way verify several features of physical reality.
New classes composite vacuum wormhole solutions of Jordan-Brans-Dicke gravitation is presented and analysed. It is shown that such solution holds for both, a bridge between separated Schwarzschild and Brans Universes and for a bridge connecting two Schwarzschild asymptotically flat regions joined by Brans throat. We have also noticed that there are some new possible candidates for wormhole spacetimes.
