We compare Mercury's precession test in standard General Relativity (GR), Brans-Dicke theories (BD), and Palatini f(R)-theories. We avoid post Newtonian (PN) approximation and compute exact precession in these theories. We show that the well-known mathematical equivalence between Palatini f(R)-theories and a specific subset of BD theories does not extend to a really physical equivalence among theories since equivalent models still allow different incompatible precession for Mercury depending on the solution one chooses. As a result one cannot use BD equivalence to rule out Palatini f(R)-theories. On the contrary, we directly discuss that Palatini f(R)-theories can (and specific models do) easily pass Solar System tests as Mercury's precession.
We study the Hamiltonian formulation of f(R) theories of gravity both in metric and in Palatini formalism using their classical equivalence with Brans-Dicke theories with a non-trivial potential. The Palatini case, which corresponds to the w=-3/2 Brans-Dicke theory, requires special attention because of new constraints associated with the scalar field, which is non-dynamical. We derive, compare, and discuss the constraints and evolution equations for the ww=-3/2 and w\neq -3/2 cases. Based on the properties of the constraint and evolution equations, we find that, contrary to certain claims in …
We study the classical Euclidean wormholes in the context of extended theories of gravity. With no loss of generality, we use the dynamical equivalence between $f(\tilde{R})$ gravity and scalar-tensor theories to construct a point-like Lagrangian in the flat FRW space time. We first show the dynamical equivalence between Palatini $f(\tilde{R})$ gravity and the Brans-Dicke theory with self-interacting potential, and then show the dynamical equivalence between the Brans-Dicke theory with self-interacting potential and the minimally coupled O'Hanlon theory. We show the existence of new Euclidean …
We shall show equivalence between Palatini-$f(\calR)$ theories and Brans-Dicke (BD) theories at the level of action principles in generic dimension with generic matter coupling. We do that by introducing the Helmholtz Lagrangian associated to Palatini-$f(\calR)$ theory and then performing frame transformations in order to recover Einstein frame and Brans-Dicke frame. This clarifies the relation among different formulations and the transformations among different frames. Additionally, it defines a formulation {\it a lá Palatini} for the Brans-Dicke theory which is dynamically equivalent to metr…
By establishing that Palatini formulation of $L(R)$ gravity is equivalent to $ω=-3/2$ Brans-Dicke theory, we show that energy-momentum tensor is covariantly conserved in this type of modified gravity theory.
A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless matter with non-vanishing modified terms together with dynamical cosmological and gravitational coupling terms. The obtained modified Einstein equations are neither those in $f(R)$ metric formalism nor the ones in $f({\cal R})$ Palatini formalism, whereas the modified source terms are {\it formally} equivalent to those of $f({\cal R})=\frac{1}{2}{\cal R}^2$ gravi…
By using the equivalence between metric and Palatini f(R) (or "modified") gravities with omega=0, -3/2 Brans-Dicke theories, it is shown that the Ehlers-Geren-Sachs theorem of general relativity is extended to modified gravity. In the case of metric f(R) gravity previously studied, this agrees with previous literature.
In this paper we shall review the equivalence between Palatini$-f(\mathcal R)$ theories and Brans- Dicke (BD) theories at the level of action principles. We shall define the Helmholtz Lagrangian associated to Palatini$-f(\mathcal R)$ theory and we will define some transformations which will be useful to recover Einstein frame and Brans-Dicke frame. We shall see an explicit example of matter field and we will discuss how the conformal factor affects the physical quantities.
We consider an approach to Brans-Dicke theory of gravity in which the scalar field has a geometrical nature. By postulating the Palatini variation, we find out that the role played by the scalar field consists in turning the space-time geometry into a Weyl integrable manifold. This procedure leads to a scalar-tensor theory that differs from the original Brans-Dicke theory in many aspects and presents some new features.
We shall discuss equivalence of frames in Palatini f(R)-theories at action level. A Palatini formulation of Brans-Dicke theories (equivalent to the purely metric ones) will also be discussed.
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.
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…
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.
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 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 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 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 discuss the validity, or lack thereof, of the Jebsen-Birkhoff theorem in scalar-tensor theories by generalizing it and regarding the Brans-Dicke-like scalar as effective matter. Both the Jordan and Einstein frames are discussed and an apparent contradiction between static spherical solutions of scalar-tensor gravity and Hawking's theorem on Brans-Dicke black holes is clarified. The results are applied to metric and Palatini f(R) gravity.
We consider a novel class of $f(\R)$ gravity theories where the connection is related to the conformally scaled metric $\hat g_{μν}=C(\R)g_{μν}$ with a scaling that depends on the scalar curvature $\R$ only. We call them C-theories and show that the Einstein and Palatini gravities can be obtained as special limits. In addition, C-theories include completely new physically distinct gravity theories even when $f(\R)=\R$. With nonlinear $f(\R)$, C-theories interpolate and extrapolate the Einstein and Palatini cases and may avoid some of their conceptual and observational problems. We further show…
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 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 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 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.
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 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.
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).
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 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.
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 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.
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 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 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
Intermediate/Extreme mass ratio inspiral (I/EMRI) system provides a good tool to test the nature of gravity in strong field. Based on the method of osculating orbits, we compute the orbital evolutions of I/EMRIs on quasi-elliptic orbits in both Einstein's general relativity and Brans-Dicke theory. The extra monopolar and dipolar channels in Brans-Dicke theory accelerate the orbital decay, so it is important to consider the effects of monopolar and dipolar emissions on the waveform. With the help of accurate orbital motion, we generate waveform templates which include both monopolar and dipolar…
Following the recent theory of Lovelock-Brans-Dicke gravity, we continue to investigate the conditions to support traversable wormholes by the gravitational effects of spacetime parity and topology, which arise from the nonminimal couplings of a background scalar field to the Chern-Pontryagin density and the Gauss-Bonnet invariant. The flaring-out condition indicates that a Morris-Thorne-type wormhole can be maintained by violating the generalized null energy condition, and thus also breaking down the generalized weak, strong, and dominant energy conditions; meanwhile, analyses of the zero-tid…
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 Brans-Dicke action is one of the most natural extensions of the Einstein-Hilbert action. It is based on the introduction of a fundamental scalar field that effectively incorporates a dynamics to the gravitational coupling $G$. In spite of the diverse motivations and the rich phenomenology that comes from its solutions, Solar System tests impose strong constraints on the Brans-Dicke theory, rendering it indistinguishable from General Relativity. In the present text, new perspectives for the Brans-Dicke theory are presented, based on the possibility that the scalar field presented in the BD …
The dynamics of the Brans-Dicke theory with a scalar field potential function is investigated. We show that the system with a barotropic matter content can be reduced to an autonomous three-dimensional dynamical system. For an arbitrary potential function we found the values of the Brans-Dicke parameter for which a global attractor in the phase space representing de Sitter state exists. Using linearized solutions in the vicinity of this critical point we show that the evolution of the Universe mimics the $Λ$CDM model. From the recent Planck satellite data, we obtain constraints on the variabil…
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 $R$.
Recently, traversable wormhole geometries were constructed in the context of f(R) gravity. The latter is equivalent to a Brans-Dicke theory with a coupling parameter w=0, which is apparently excluded from the narrow interval, -3/2<w<-4/3, extensively considered in the literature of static wormhole solutions in vacuum Brans-Dicke theory. However, this latter interval is only valid for a specific choice of an integration constant of the field equations derived on the basis of a post-Newtonian weak field approximation, and there is no reason for it to hold in the presence of compact objects with …
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.
In this paper we analyze the signal emitted by a compact binary system in the Jordan-Brans-Dicke theory. We compute the scalar and tensor components of the power radiated by the source and study the scalar waveform. Eventually we consider the detectability of the scalar component of the radiation by interferometers and resonant-mass detectors.
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.
