There exist gravitational memory effects in Brans-Dicke theory. They are closely related to the Bondi-Metzner-Sachs symmetries living on the null infinity in an isolated system. By studying the asymptotically flat spacetime in Brans-Dicke theory and the asymptotic symmetries, one discovers that the displacement memory effect in the tensor sector is due to the vacuum transition caused by the null energy fluxes panetrating the null infinity, while in the scalar sector, the vacuum transition is due to the angular momentum fluxes. Together with the spin and the center-of-mass memory effects, the displacement memories are constrained by various flux-balance laws.
We argue that a version of the four dimensional Brans-Dicke theory can be embedded in the standard flat spacetime electroweak theory. The embedding involves a change of variables that separates the isospin from the hypercharge in the electroweak theory.
We discuss the viability of $f(R)$ and Brans-Dicke theories of gravity in light of the recent Swampland conjectures. We show that in the case of perfect fluid domination the swampland conjecture conditions may be easily satisfied and therefore we focus on the constraints in the vacuum theory. We derive the conditions for the swampland conjectures in $f(R)$ and Brans-Dicke framework, and find that a large portion of the parameter space is not allowed. Furthermore, we analyze particular $f(R)$ models of inflation and dark energy and in their case we set the allowed range of $R$.
The conformal structure of Brans-Dicke gravity action is carefully studied. It is discussed that Brans-Dicke gravity action has definitely no conformal invariance. It is shown, however, that this lack of conformal invariance enables us to demonstrate that Brans-Dicke theory appears to have a better short-distance behavior than Einstein gravity as far as Euclidean path integral formulation for quantum gravity is concerned.
We investigate an alternative compactification of extra dimensions using local cosmic string in the Brans-Dicke gravity framework. In the context of dynamical systems it is possible to show that there exist a stable field configuration for the Einstein-Brans-Dicke equations. We explore the analogies between this particular model and the Randall-Sundrum scenario.
A five dimensional brane cosmology with non-minimally coupled scalar field to gravity has been considered in a Jordan-Brans-Dicke frame. We derive an effective four dimensional field equations on a 3+1 dimensional brane where the fifth dimension has been assumed to have an orbifold symmetry. We have noticed that the evolution equation for the matter component stuck to the brane is non-trivially coupled to the scalar field living on the brane and the bulk. Finally we discuss some cosmological consequences of this set-up.
We study cosmological application of the holographic energy density in the Brans-Dicke theory. Considering the holographic energy density as a dynamical cosmological constant, it is more natural to study it in the Brans-Dicke theory than in general relativity. Solving the Friedmann and Brans-Dicke field equations numerically, we clarify the role of Brans-Dicke field during evolution of the universe. When the Hubble horizon is taken as the IR cutoff, the equation of state ($w_{\Lmd}$) for the holographic energy density is determined to be 5/3 when the Brans-Dicke parameter $\omg$ goes infinity.…
We provide a detailed description for power-law scaling FRW cosmological models in Brans-Dicke theory dominated by two interacting fluid components during the expansion of the universe.
We interpret the Brans-Dicke gravity from entropic viewpoint. We first apply the Verlinde's entropic formalism in the Einstein frame, then perform the conformal transformation which connects the Einstein frame to the Jordan frame. The transformed result yields the equation of motion of the Brans-Dicke theory in the Jordan frame.
We review some recent results obtained from the application of the Gauss-Codazzi formalism to brane-worlds models in the Brans-Dicke gravity. The cases of 4-branes embedded in a six-dimensional with and without $\mathbb{Z}_{2}$ symmetry are both analyzed.
We have shown that the dynamics of the scalar field $ϕ(x)= ``G^{-1}(x)"$ in Brans-Dicke theories of gravity makes the surface area of the black hole horizon {\it oscillatory} during its dynamical evolution. It explicitly explains why the area theorem does not hold in Brans-Dicke theory. However, we show that there exists a certain non-decreasing quantity defined on the event horizon which is proportional to the black hole entropy for the case of stationary solutions in Brans-Dicke theory. Some numerical simulations have been demonstrated for Oppenheimer-Snyder collapse in Brans-Dicke theory.
It has recently been argued that non-trivial Brans-Dicke black hole solutions different from the usual Schwarzschild solution could exist. We attemt here to ``censor'' these non-trivial Brans-Dicke black hole solutions by examining their thermodynamic properties. Quantities like Hawking temperature and entropy of the black holes are computed. Analysis of the behaviors of these thermodynamic quantities appears to show that even in Brans-Dicke gravity, the usual Schwarzschild spacetime turns out to be the only physically relevant uncharged static black hole solution.
We find a self-gravitating monopole and its black hole solution in Brans-Dicke theory. We mainly discuss the properties of these solutions in the Einstein frame and compare the solutions with those in general relativity.
We look for a Brans-Dicke type of generalization of the Horava-Lifshitz gravity. It is shown that such a generalization is possible within the detailed balance condition. Classically, the resulting theory reduces in the IR limit to the usual Brans-Dicke theory with a negative cosmological constant for certain values of parameters. We then consider homogeneous and isotropic cosmology and study the effects of the new terms appearing in the model.
We consider a five dimensional DGP-brane scenario endowed with a non-minimally coupled scalar field within the context of Brans-Dicke theory. This theory predicts that the mass appearing in the gravitational potential is modified by the addition of the mass of the effective intrinsic curvature on the brane. We also derive the effective four dimensional field equations on a 3+1 dimensional brane where the fifth dimension is assumed to have an orbifold symmetry. Finally, we discuss the cosmological implications of this setup, predicting an accelerated expanding universe with a value of the Brans…
In this Letter it is shown that when the holographic dark energy is combined with the Brans-Dicke field equations the transition from decelerated to accelerated expansion of the Universe can be more easily accounted for than when resort to the Einstein field equations is made. Likewise, the coincidence problem of late cosmic acceleration gets more readily softened.
The equivalence between f(R) gravity and scalar-tensor theories is invoked to study the null, strong, weak and dominant energy conditions in Brans-Dicke theory. We consider the validity of the energy conditions in Brans-Dicke theory by invoking the energy conditions derived from a generic f(R) theory. The parameters involved are shown to be consistent with an accelerated expanding universe.
We present the static, spherically symmetric solutions of the low energy $d = 4$ string. They form a simple generalisation of the Schwarzschild solution and describe the gravitational field of a spherical star in perturbative string theory. If the Robertson parameter $γ$ is different from one, these solutions describe singular objects with naked singularities at their horizons, and whose Hawking temperature is infinite. These objects might represent ``massive remnants'', the end states of black holes. Our analysis also implies that Brans-Dicke theory has a naked singularity. Invoking cosmic ce…
Within the framework of Brans-Dicke gravity, we investigate inflation with the quartic potential, $λφ^4/4$, in the presence of generalized Brans-Dicke parameter $ω_{\rm GBD}(φ)$. We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of general form of the potential $U(φ)$ and $ω_{\rm GBD}(φ)$. For the quartic potential, our results show that the predictions of the model are in well agreement with the Planck 2015 data for the generalized Brans-Dicke …
We study responses of the Brans-Dicke field due to gravitational collapses of scalar field pulses using numerical simulations. Double-null formalism is employed to implement the numerical simulations. If we supply a scalar field pulse, it will asymptotically form a black hole via dynamical interactions of the Brans-Dicke field. Hence, we can observe the responses of the Brans-Dicke field by two different regions. First, we observe the late time behaviors after the gravitational collapse, which include formations of a singularity and an apparent horizon. Second, we observe the fully dynamical b…
We propose a unimodular version of the Brans-Dicke theory designed with a constrained Lagrangian formulation. The resulting field equations are traceless. The vacuum solutions in the cosmological background reproduce the corresponding solutions of the usual Brans-Dicke theory but with a cosmological constant term. A perturbative analysis of the scalar modes is performed and stable and unstable configurations appear in contrast with the Brans-Dicke case for which only stable configurations occur. On the other hand, tensorial modes in this theory remains the same as in the traditional Brans-Dick…
We study the Brans-Dicke model in the presence of an axion. The dynamical equations are solved when the fields are space independent and the metric is spatially flat. It is found that at late time the scale factor undergoes decelerated expansion but the dilaton grows large. At early time, scale factor and the dilaton approach constants.
We study the cosmology of the Brans-Dicke theory with perfect fluid type matter. In our previous work, we found exact solutions for any Brans-Dicke parameter $ω$ and for general parameter $γ$ of equation of state. In this paper we further study the cosmology of these solutions by analyzing them according to their asymptotic behaviors. The cosmology is classified into 19 phases according to the values of $γ$ and $ω$. The effect of the cosmological constant to the Brans-Dicke theory is a particular case of our model. We give plot of time evolution of the scale factor by numerical investigations.…
We study the collapse of a free scalar field in the Brans-Dicke model of gravity. At the critical point of black hole formation, the model admits two distinctive solutions dependent on the value of the coupling parameter. We find one solution to be discretely self-similar and the other to exhibit continuous self-similarity.
We study the dynamics of false vacuum bubbles in the Brans-Dicke theory of gravity by using the thin shell or thin wall approximation. We consider a false vacuum bubble that has a different value for the Brans-Dicke field between the inside false vacuum region and the outside true vacuum region. Within a certain limit of field values, the difference of field values makes the effective tension of the shell negative. This allows new expanding false vacuum bubbles to be seen by the outside observer, which are disallowed in Einstein gravity.
We obtain geodesically complete spacetimes generated by static and rotating magnetic point sources in an Einstein-Maxwell-Dilaton theory of the Brans-Dicke type in three dimensions (3D). The theory is specified by three fields, the dilaton, the graviton and the electromagnetic field, and two parameters, the cosmological constant and the Brans-Dicke parameter, w. When the Brans-Dicke parameter is infinity, our solution reduces to the magnetic counterpart of the BTZ solution, while the w=0 case is equivalent to 4D general relativity with one Killing vector. The source for the magnetic field can …
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 study the Brans-Dicke theory of gravity in Riemann-Cartan space-times, and obtain general torsion solutions, which are completely determined by Brans-Dicke scalar field $Φ$, in the false vacuum energy dominated epoch. The substitution of the torsion solutions back to our action gives the original Brans-Dicke action with $Φ$-dependent Brans-Dicke parameter $ω(Φ)$. The evolution of $ω(Φ)$ during the inflation is studied and it is found that $ω$ approaches to infinity at the end of inflation. This may solve the $ω$-problem in the extended inflation model.
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 …
We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
We consider the quantum gravity and cosmology of a Jordan-Brans-Dicke theory, predicted by string effective actions. We study its canonical formalism and find that the constraint algebra is that of general relativity, as a consequence of the general covariance of scalar-tensor theories. We also analyze the problem of boundary conditions and propose that they must be imposed in the Jordan frame, in which particles satisfy the strong equivalence principle. Specifically, we discuss both Hartle-Hawking and wormhole boundary conditions in the context of quantum cosmology. We find quantum wormhole s…
Higher dimensional, static, cylindrically symmetric vacuum solutions with and without a cosmological constant in the Brans-Dicke theory are presented. We show that, for a negative cosmological constant and for specific values of the parameters, a particular subclass of these solutions include higher dimensional topological black hole-type solutions with a flat horizon topology. We briefly extend our discussion to stationary vacuum and $Λ-$vacuum solutions.
We consider the Brans-Dicke theory motivated by the $f(R) = R + αR^n - βR^{2-n}$ model to obtain a stable minimum of the Einstein frame scalar potential of the Brans-Dicke field. As a result we have obtained an inflationary scalar potential with non-zero value of residual vacuum energy, which may be a source of Dark Energy. In addition we discuss the probability of quantum tunnelling from the minimum of the potential. Our results can be easily consistent with PLANCK or BICEP2 data for appropriate choices of the value of $n$ and $ω$.
We consider a modified Brans-Dicke theory in which except the usual Brans-Dicke parameter a new dimensionful parameter appears which modifies the kinetic term of the scalar field coupled to gravity. Solving the coupled Einstein-Klein-Gordon equations we find new spherically symmetric solutions. Depending on the choices of the parameters these solutions reduce to the Schwarzschild solution of General Relativity and they give new wormhole solutions which depend on the new parameter.
We consider a modification of the Brans-Dicke gravitational Action Integral inspired by the existence of a minimum length uncertainty for the scalar field. In particular, the kinetic part of the Brans-Dicke scalar field is modified such that the equation of motion for the scalar field be modified according to the quadratic Generalized Uncertainty Principle (GUP). For the background geometry, we assume the homogeneous and isotropic Friedmann--Lema\^ıtre--Robertson--Walker metric. We investigate the dynamics and the cosmological evolution for the dynamical variables of the theory and we compare …
We study the cosmology of the Brans-Dicke(BD) theory coupled to perfect fluid type matter. In our previous works, the case where matter is coming from the Ramond-Ramond sector of the string theory was studied. Here, we study the case where matter is coming from the NS-NS sector. Exact solutions are found and the cosmology is classified according to the values of $γ$, the parameter of the equation of state and $ω$, Brans-Dicke parameter. We find taht, in string frame, there are solutions without singularity for some ranges of $γ$ and $ω$. In Einstein frame, however, all solutions are singular.
In this paper, conditions for existence of Gödel and Gödel-type solutions in Brans-Dicke (BD) scalar-tensor theory and their main features are studied. The consistency of equations of motion, causality violation and existence of CTCs (closed time-like curves) are investigated. The role which cosmological constant and Mach principle play to achieve the consistency of this model is studied.
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 consider a modified ``Swiss cheese'' model in the Brans-Dicke theory, and discuss the evolution of black holes in the expanding universe. We define the black hole radius by the Misner-Sharp mass and find the time evolution for dust and vacuum universes.
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.
Existence check of non-trivial, stationary axisymmetric black hole solutions in Brans-Dicke theory of gravity in different direction from those of Penrose, Thorne and Dykla, and Hawking is performed. Namely, working directly with the known explicit spacetime solutions in Brans-Dicke theory, it is found that non-trivial Kerr-Newman-type black hole solutions different from general relativistic solutions could occur for the generic Brans-Dicke parameter values -5/2\leq ω<-3/2. Finally, issues like whether these new black holes carry scalar hair and can really arise in nature and if they can, what…
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.
The five dimensional Brans-Dicke theory naturally provides two scalar fields by the Killing reduction mechanism. These two scalar fields could account for the accelerated expansion of the universe. We test this model and constrain its parameter by using the type Ia supernova (SN Ia) data. We find that the best fit value of the 5-dimensional Brans-Dicke coupling contant is $ω= -1.9$. This result is also consistent with other observations such as the baryon acoustic oscillation (BAO).
We study longstanding problem of cosmological clock in the context of Brans-Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogenous cosmological models. Then, we show that formulation of the Brans-Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the Friedmann-Robertson-Walker cosmological models.
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.
Conformal relativity theory which is also known as Hoyle-Narlikar theory has recently been given some new interest. It is an extended relativity theory which is invariant with respect to conformal transformations of the metric. In this paper we show how conformal relativity is related to the Brans-Dicke theory and to the low-energy-effective superstring theory. We show that conformal relativity action is equaivalent to a transformed Brans-Dicke action for Brans-Dicke parameter $ω= -3/2$ in contrast to a reduced (graviton-dilaton) low-energy-effective superstring action which corresponds to a B…
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 consider a modified ``Swiss cheese'' model in Brans-Dicke theory, and use it to discuss the evolution of black holes in an expanding universe. We define the black hole radius by the Misner-Sharp mass and find their exact time evolutions for dust and vacuum universes of all curvatures.
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.
In this paper we study emergent universe model in the context of a self interacting Jordan-Brans-Dicke theory. The model presents a stable past eternal static solution which eventually enters a phase where the stability of this solution is broken leading to an inflationary period. We also establish constraints for the different parameters appearing in our model.
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.
We show that cosmological sudden singularities that respect the energy conditions can occur at finite times in Brans-Dicke and more general scalar-tensor theories of gravity. We construct these explicitly in the Friedmann universes. Higher-order versions of these singularities are also possible, including those that arise with when scalar fields have a self-interaction potential of power-law form.7 pages, no figures
