On the Stability of Jordan-Brans-Dicke Static Universe
Sergio del Campo, Ramon Herrera, Pedro Labrana
备注：
24 pages, 2 figures, typos corrected, some improvements in section 4 and comments added in conclusions. References added. Accepted for publication in JCAP
In this work we study the stability of the Jordan-Brans-Dicke (JBD) static universe. This is motivated by the possibility that the universe might have started out in an asymptotically JBD static state, in the context of the so called emergent universe scenario. We extent our previous results on stability of JBD static universe by considering spatially homogeneous Bianchi type IX anisotropic perturbation modes and by including more general perfect fluids. Contrary to general relativity, we have found that the JBD static universe, dominated by a standard perfect fluid, could be stable against isotropic and anisotropic perturbations. The implications of these results for the initial state of the universe and its pre-inflationary evolution are discussed.
Jordan and Einstein frame are studied under the light of Hamiltonian formalism. Dirac's constraint theory for Hamiltonian systems is applied to Brans-Dicke theory in the Jordan Frame. In both Jordan and Einstein frame, Brans-Dicke theory has four secondary first class constraints and their constraint algebra is closed. We show, contrary to what is generally believed, the Weyl (conformal) transformation, between the two frames, is not a canonical transformation, in the sense of Hamiltonian formalism. This addresses quantum mechanical inequivalence as well. A canonical transformation is shown.
In this work we study an alternative scheme for an Emergent Universe scenario in the context of a Jordan-Brans-Dicke theory, where the universe is initially in a truly static state supported by a scalar field located in a false vacuum. The model presents a classically stable past eternal static state which is broken when, by quantum tunneling, the scalar field decays into a state of true vacuum and the universe begins to evolve following the extended open inflationary scheme.
The Hamiltonian of any quantum cosmological model must obey some conditions in order to be self-adjoint, or to admit self-adjoint extensions. We will consider in this paper the self-adjoint character of the Hamiltonian resulting from the Brans-Dicke theory, both in Einstein and Jordan frames. In both cases we find the wave-function solutions in order to obtain concrete predictions for the evolution of the Universe. We show that the specific cosmological scenarios obtained depend very weakly on the conditions of having a self-adjoint operator. The problem of equivalence between Einstein and Jor…
With an explicit example, we show that Jordan frame and the conformally transformed Einstein frames clearly lead to different physics for a non-minimally coupled theory of gravity, namely Brans-Dicke theory, at least at the quantum level. The example taken up is the spatially flat Friedmann cosmology in Brans-Dicke theory.
We investigate a Jordan-Brans-Dicke (JBD) scalar field, $Φ$, with power-law potential in the presence of a second scalar field, $ϕ$, 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 $ϕ$ 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 $a(t)\simeq e^{α_1 t^{p_1}}$, as $t\ri…
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 $ω$ from the Cassini …
In recent years, gravitational models motivated by quantum corrections to gravity which introduce higher order terms like $R^{2}$ or terms in which the Riemann tensor is not symmetric have been studied by several authors in the form of a general Brans-Dicke type model containing the Ricci scalar, the Holst term and the Nieh-Yan invariant. In this paper we focus on the less explored Jordan frame of such theories and in the comparison between both this frame and the Einstein one. Furthermore, we discuss the role of the transformation of the torsion under conformal transformations and show that t…
In this work, we present a complete analysis of the quantisation of the classical Brans-Dicke Theory using the method of affine quantisation in the Hamiltonian description of the theory. The affine quantisation method is based on the symmetry of the phase-space of the system, in this case the (positive) half-plane, that is identified with the affine group. We consider a FLRW-type spacetime, and since the scale factor is always positive, the affine method seems to be more suited than the canonincal quantisation for our Quantum Cosmology. We find the wave function of the Brans-Dicke universe, an…
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…
Approximate vacuum solutions of Jordan-Brans-Dicke theory for perturbed scalar field and perturbed Robertson-Walker metric, are found. Solutions for the scale factor and the scalar field in unperturbed JBD theory are dependent on the $ω$ parameter which determines how the scalar field is coupled to geometry of space-time. After adding a metric perturbation to Robertson-Walker metric and a perturbation to the scalar field, we solved the linearized JBD equations and found the scale factor and the scalar field as $a\propto t$ and $ϕ\propto t^{-2}$ with $ω=$-3/2. The results are necessary conditio…
We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics equations on the target space of the nonlinear sigma-model. The analytical solutions in elliptical functions are obtained when the conformal couplings are given by reciprocal exponential functions. The behavior of the scale factor in the Jordan frame is studied using numerical computations. For certain parameters the solutions can describe an accelerated expansio…
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 investigate a field theoretical approach to the Jordan-Brans- Dicke (JBD) theory extended with a particular potential term on a cosmological background by starting with the motivation that the Higgs field and the scale factor of the universe are related. Based on this relation, it is possible to come up with mathematically equivalent but two different interpretations. From one point of view while the universe is static, the masses of the elementary particles change with time. The other one, which we stick with throughout the manuscript, is that while the universe is expanding, particle mass…
Recently the most general completion of Brans-Dicke theory was appeared with energy exchanged between the scalar field and ordinary matter, given that the equation of motion for the scalar field keeps the simple wave form of Brans-Dicke. This class of theories contain undetermined functions, but there exist only three theories which are unambiguously determined from consistency. Here, for the first such theory, it is found the action of the vacuum theory which arises as the limit of the full matter theory. A symmetry transformation of this vacuum action in the Jordan frame is found which consi…
We provide an end-to-end exploration of a distinct modified gravitational theory in Jordan-Brans-Dicke (JBD) gravity, from an analytical and numerical description of the background expansion and linear perturbations, to the nonlinear regime captured with a hybrid suite of $N$-body simulations, to the parameter constraints from existing cosmological probes. The nonlinear corrections to the matter power spectrum due to baryons, massive neutrinos, and modified gravity are simultaneously modeled and propagated in the cosmological analysis for the first time. In the combined analysis of the Planck …
