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Register a new userVacuum Brans-Dicke theory in the Jordan and Einstein frames: can they be distinguished by lensing?
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Vacuum Brans-Dicke 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. Despite this, the conformal frames are inequivalent describing different geometries. It is shown that the predictions of the weak field lensing (WFL) observables in the EF are different from those recently obtained in the JF for the vacuum Brans-Dicke class 1 solution. The value of the Brans-Dicke coupling parameter $omega$ from the Cassini spacecraft experiment reveals the degree of accuracy needed to experimentally distinguish the WFL measurements including the total magnification factor in the two frames.
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When Brans-Dicke Theory is formulated in terms of the Jordan scalar field phi, dark energy is related to the mass of this field. We show that if phi is taken to be a complex scalar field then an exact solution of the vacuum equations shows that Friedmann equation possesses a term, proportional to the inverse sixth power of the scale factor, as well as a constant term. Possible interpretations and phenomenological implications of this result are discussed.
We investigate a Jordan-Brans-Dicke (JBD) scalar field, $Phi$, with power-law potential in the presence of a second scalar field, $phi$, with an exponential potential, in both the Jordan and the Einstein frames. We present the relation of our model with the induced gravity model with power-law potential and the integrability of this kind of models is discussed when the quintessence field $phi$ is massless, and has a small velocity. We prove that in JBD theory, the de Sitter solution is not a natural attractor but an intermediate accelerated solution of the form $a(t)simeq e^{alpha_1 t^{p_1}}$, as $trightarrow infty$ where $alpha_1>0$ and $0<p_1<1$, for a wide range of parameters. Furthermore, in the Einstein frame we get that the attractor is also an intermediate accelerated solution of the form $mathfrak{a}(mathfrak{t})simeq e^{alpha_2 mathfrak{t}^{p_2}}$ as $mathfrak{t}rightarrow infty$ where $alpha_2>0$ and $0<p_2<1$, for the same conditions on the parameters as in the Jordan frame. In the special case of a quadratic potential in the Jordan frame, or for a constant potential in the Einsteins frame, these solutions are of saddle type. Finally, we present a specific elaboration of our extension of the induced gravity model in the Jordan frame, which corresponds to a linear potential of $Phi$. The dynamical system is then reduced to a two dimensional one, and the late-time attractor is linked with the exact solution found for the induced gravity model. In this example the intermediate accelerated solution does not exist, and the attractor solution has an asymptotic de Sitter-like evolution law for the scale factor. Apart from some fine-tuned examples such as the linear, and quadratic potential ${U}(Phi)$ in the Jordan frame, it is true that intermediate accelerated solutions are generic late-time attractors in a modified JBD theory.
We use cosmic microwave background data from WMAP, ACBAR, VSA and CBI, and galaxy power spectrum data from 2dF, to constrain flat cosmologies based on the Jordan-Brans-Dicke theory, using a Markov Chain Monte Carlo approach. Using a parametrization based on xi=1/4omega, and performing an exploration in the range lnxi in [-9,3], we obtain a 95% marginalized probability bound of lnxi < -6.2, corresponding to a 95% marginalized probability lower bound on the Brans-Dicke parameter omega>120.
It is shown that the Jordan frame and its conformally transformed version, the Einstein frame of nonminimally coupled theories of gravity, are actually equivalent at the quantum level. The example of the theory taken up is the Brans-Dicke theory, and the wave packet calculations are done for a homogeneous and isotropic cosmological model in the purest form of the theory, i.e., in the absence of any additional matter sector. The calculations are clean and exact, and the result obtained are unambiguous.
Since the evidence for an accelerated universe and the gap of 70% in the total energy, collected by WMAP, search for alternatives for the general relativity is an important issue, for this theory is not suited for these new phenomena. A particular alternative is the Brans-Dicke theory which has being allowing inspiring results, for example, concerning k-essence type fields in 4 dimensions. However, this theory is almost unexplored in the context of the dimensional reduction of the theory in 3 dimensions. In this work, we address some problems in this dimensional reduction, namely, evaluation of the deceleration parameter of the universe described by the 3 dimensional Brans-Dicke with and without matter. In both cases, we see that it is not possible to consider the theory as a model of k-essence descrybing the dark energy, but it can be considered as descrybing the dark matter.
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