Vacuum Brans-Dicke Theory Research Articles

Vacuum Brans–Dicke theory in the Jordan and Einstein frames: Can they be distinguished by lensing?

Vacuum Brans-Dicke (BD) theory continues to receive widespread attention since it is consistent with solar and cosmological experiments. The theory can be self-consistently described in two frames, the Jordan frame (JF) and the conformally rescaled Einstein frame (EF), the transformations providing an easy passage from one frame to the other at the level of actions and solutions. While coordinate transformations do not change curvature properties, conformal transformations do change them leading to corresponding changes in the numerical values of observables. A previous article by Bhadra et al.[Formula: see text] did exemplify this change between JF and EF using the diagnostic of second-order light deflection. This important work leaves room for further improvements on two points, which we do here. First, the measurement of second-order effect faced technically unsurmountable difficulties even around the Sun, hence actually abandoned. Second, the comparison of quantitative values between JF and EF should be based on a common value of [Formula: see text] connecting the two frames. Keeping these in mind, we investigate a technically easier diagnostic, viz., the weak field lensing (WFL) and compare the quantitative changes at common [Formula: see text] to show that the two frames can indeed be distinguished by lensing experiments. Specifically, the predictions of light deflection, image position, total magnification and magnification factor are computed in the EF and compared with those recently obtained (by Gao et al.[Formula: see text]) directly in the JF BD class I solution. The use of the value of BD coupling constant [Formula: see text], suggested by the Cassini spacecraft solar experiment, reveals that an exceptionally high degree of accuracy is needed to experimentally rule out one or the other frame by means of WFL measurements.

Regular Solutions in Vacuum Brans-Dicke Theory Compared to Vacuum Einstein Theory

We will confront some static spherically symmetric vacuum Brans-Dicke solutions in the Jordan and Einstein Frames with the Robertson parameters. While the regular solution in the vacuum Einstein theory is just the Schwarzschild black hole, the same in the Jordan frame Brans-Dicke theory is shown to represent not a black hole but a traversable wormhole. But, in this case, the valid range ofωbecomes too narrow to yield the observed weak field Robertson parameters at the positive mass mouth. The corresponding solution in the Einstein frame also provides a regular wormhole, and it yields the correct parametric values but only up to “one and half order.” We argue that a second-order contribution can in principle distinguish between the signatures of the regular wormhole and the singular Buchdahl solution in the Einstein frame. Thus, at the level of regular solutions, Brans-Dicke theory in each frame predicts effects very different from those of Einstein's theory. To our knowledge, these theoretical distinctions seem not to have received adequate attention so far.

FRW cosmology from five dimensional vacuum Brans–Dicke theory

We follow approach of induced matter theory for 5D vacuum BD, introduce induced matter and potential in 4D hypersurfaces, and employ generalized FRW type solution. We confine ourselves to scalar field and scale factors be functions of the time. This makes the induced potential, by its definition, vanishes. When the scale factor of fifth dimension and scalar field are not constants, 5D eqs for any geometry admit a power law relation between scalar field and scale factor of fifth dimension. Hence the procedure exhibits that 5D vacuum FRW like eqs are equivalent, in general, to corresponding 4D vacuum ones with the same spatial scale factor but new scalar field and coupling constant. We show that 5D vacuum FRW like eqs or its equivalent 4D vacuum ones admit accelerated solutions. For constant scalar field, eqs reduce to usual FRW eqs with typical radiation dominated universe. For this situation we obtain dynamics of scale factors for any geometry without any priori assumption. For nonconstant scalar fields and spatially flat geometries, solutions are found to be power law and exponential ones. We also employ weak energy condition for induced matter, that allows negative/positive pressures. All types of solutions fulfill WEC in different ranges. The power law solutions with negative/positive pressures admit both decelerating and accelerating ones. Some solutions accept shrinking extra dimension. By considering nonghost scalar fields and recent observational measurements, solutions are more restricted. We illustrate that accelerating power law solutions, which satisfy WEC and have nonghost fields, are compatible with recent observations in ranges -4/3 < \omega </- -1.3151 and 1.5208 </- n < 1.9583 for dependence of fifth dimension scale factor with usual scale factor. These ranges also fulfill condition nonghost fields in the equivalent 4D vacuum BD eqs.

General class of vacuum Brans-Dicke wormholes

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 strong gravitational fields. In this context, we construct a general class of vacuum Brans-Dicke wormholes that include the value of w=0. Furthermore, we present the general condition for the existence of vacuum Brans-Dicke wormhole geometries, and show that the presence of effective negative energy densities is a generic feature of these vacuum solutions.

Late time cosmic acceleration from vacuum Brans–Dicke theory in 5D

We show that the scalar-vacuum Brans–Dicke equations in 5D are equivalent to Brans–Dicke theory in 4D with a self-interacting potential and an effective matter field. The cosmological implication, in the context of FRW models, is that the observed accelerated expansion of the universe comes naturally from the condition that the scalar field is not a ghost, i.e. ω > −3/2. We find an effective matter-dominated 4D universe which shows accelerated expansion if −3/2 < ω < −1. We study the question of whether accelerated expansion can be made compatible with large values of ω, within the framework of a 5D scalar-vacuum Brans–Dicke theory with variable, instead of constant, parameter ω. In this framework, and based on a general class of solutions of the field equations, we demonstrate that accelerated expansion is incompatible with large values of ω.

On static spherically symmetric solutions of the vacuum Brans-Dicke theory

It is shown that among the four classes of the static spherically symmetric solution of the vacuum Brans-Dicke theory of gravity only two are really independent. Further by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only Brans class I solution with certain restriction on solution parameters may represent exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwarzschild black hole is available in the Brans-Dicke theory.

WORMHOLES IN VACUUM BRANS–DICKE THEORY

It is shown that among the different classes of claimed static wormhole solutions of the vacuum Brans–Dicke theory only Brans Class I solution with coupling constant ω less than -1.5 (excluding the point ω = 2) gives rise to physically viable traversable wormhole geometry. Usability of this wormhole geometry for interstellar travel has been examined.

New Brans-Dicke wormholes

Two new classes of exact solutions in vacuum Brans-Dicke theory are obtained, each of which is a two-way traversable wormhole for the coupling parameter $\ensuremath{\omega}&lt;\ensuremath{-}2$ or $\ensuremath{-}2&lt;\ensuremath{\omega}&lt;~0,$ respectively. Each of the two new classes of exact solutions satisfies not only the general constraints given by Morris and Thorne [Am. J. Phys. 56, 395 (1988)], as concluded earlier, but also the constraints from a trip through a wormhole. It also follows that the scalar field $\ensuremath{\varphi}$ plays the role of exotic matter violating the weak energy condition.

VACUUM BRANS–DICKE THEORY AND WORMHOLES

This paper deals with vacuum Brans–Dicke theory in an anisotropic Kantowski–Sachs model and Euclidean wormhole solutions have been obtained. The Wheeler–Dewitt (WD) equation has been solved using separable form of the wave function and these solutions have been examined whether wormhole boundary condition due to Hawking is satisfied or not.

A New Traversable Wormhole Solution in Vacuum Brans-Dicke Theory

A new set of exact solutions in vacuum Brans-Dicke theory is obtained, which is a tow-way traversable wormhole for the coupling parameter ω (ω < -2). This new set of exact solutions satisfies not only the general constraints on the shape function b(R) and the redshift function Φ(R) given by Morris and Thorne [Am. J. Phys. 56 (1988) 395], but also the constraints on them from a trip through wormhole. It also follows that the scalar field φ plays a role of exotic matter violating the weak energy condition.

A NEW TWO-WAY TRAVERSABLE WORMHOLE SOLUTION FOR VACUUM BRANS-DICKE EQUATIONS

It is shown that a new set of exact solutions in vacuum Brans-Dicke theory is obtained and it admits wormhole geometry.Two-way traversable wormholes in the Brans-Dicke theory is allowed for the coupling parameter ω(-2≤ω≤0) and the appropriately chosen integration constants.It also follows that the scalar field  plays the role of exotic matter and this violates the weak energy condition.

Effects of anisotropy and spatial curvature on the pre-big-bang scenario

A class of exact, anisotropic cosmological solutions to the vacuum Brans-Dicke theory of gravity is considered within the context of the pre-big-bang scenario. Included in this class are the Bianchi type III, V and ${\mathrm{VI}}_{h}$ models and the spatially isotropic, negatively curved Friedmann-Robertson-Walker universe. The effects of large anisotropy and spatial curvature are determined. In contrast with a negatively curved Friedmann-Robertson-Walker model, there exist regions of the parameter space in which the combined effects of curvature and anisotropy prevent the occurrence of inflation. When inflation is possible, the necessary and sufficient conditions for successful pre-big-bang inflation are more stringent than in the isotropic models. The initial state for these models is established and corresponds in general to a gravitational plane wave.

BRANS–DICKE AND RELATED EUCLIDEAN WORMHOLES

In a recent paper1 Euclidean wormhole solution has been obtained with a vacuum Brans–Dicke theory with parameter ω=0. These wormholes suffer from unphysical values of the gravitational constant. One can relate the various known wormholes by means of conformal transformations; although one should not transform them directly to the Einstein frame as the gravitational constant there is "forced" physical: so removing the wormholes. However, by arguing for the existence of a fundamental minimum length scale such wormholes can now be considered as representative of quantum gravitational phenomena. One can also obtain wormholes as solutions of the quantum mechanical Wheeler–De Witt equation; now in Brans–Dicke for any ω&gt;-3/2.

Brans-Dicke wormholes in the Jordan and Einstein frames

We examine the possibility of static wormhole solutions in the vacuum Brans-Dicke theory both in the original (Jordan) frame and in the conformally rescaled (Einstein) frame. It turns out that, in the former frame, wormholes exist only in a very narrow interval of the coupling parameter, viz., $\ensuremath{-}3/2l\ensuremath{\omega}l\ensuremath{-}4/3.$ It is shown that these wormholes are not traversable in practice. In the latter frame, wormhole solutions do not exist at all unless energy conditions are violated by hand.

New Exact Vacuum Solutions in Brans–Dicke Theory

A family of exact solutions to vacuum Brans–Dicke theory with spherical symmetry is found. In the limit of large ω this family reduces to the solutions obtained in general relativity with a scalar field. The solutions show curvature singularities for all times, therefore they do not represent the gravitational collapse of a physical system with regular initial data in the theory. One would like to interpret it as an inhomogeneous dynamical cosmology, but the lack of a regular spacelike slice forbids it. For a special value of an integration constant we have an isotropic cosmological model without the problems mentioned above.

Instability of an “approximate black hole”

We investigate the stability of a family of spherically symmetric static solutions in vacuum Brans-Dicke theory (with $\omega=0$) recently described by van Putten. Using linear perturbation theory, we find one exponentially growing mode for every member of the family of solutions, and thus conclude that the solutions are not stable. Using a previously constructed code for spherically symmetric Brans-Dicke, additional evidence for instability is provided by directly evolving the static solutions with perturbations. The full non-linear evolutions also suggest that the solutions are black-hole-threshold critical solutions.

Wormholes in vacuum Brans-Dicke theory

We present a Euclidean wormhole solution in vacuum Brans-Dicke theory, which is different from that obtained by Accetta et al. This wormhole appears to have the feature that its throat dimension increases linearly with Euclidean cosmic time, although this increase may not be measurable. It also requires a negative Brans-Dicke parameterω.

Wormhole Solution in Vacuum Brans-Dicke Theory with Cosmological Constant

In this paper, we give an Euclidean wormhole solution in the Brans-Dicke theory with cosmological constant. We show that this wormhole is unlike all the others, its configuration is non-static. The throat radius of the wormhole will increase as Euclidan cosmic time increases.

WORMHOLE SOLUTION IN VACUUM REAL BRANS-DICKE THEORY

In this paper, we give an Euclidean wormhole solution in the vacuum Brans-Dicke theory, which is different from that obtained by Accetta et al. We show that this wormhole unlike all the others, it's throat dimension increases linearly with the increasing of the Euclidean cosmic time.