Dicke Field Research Articles

Impact of star pressure on γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} in modified gravity beyond post-Newtonian approach

We offer a concrete example exhibiting marked departure from the Parametrized Post-Newtonian (PPN) approximation in a modified theory of gravity. Specifically, we derive the exact formula for the Robertson parameter γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} in Brans–Dicke gravity for spherical compact stars, explicitly incorporating the pressure content of the stars. We achieve this by exploiting the integrability of the 00-component of the Brans–Dicke field equation. In place of the conventional PPN result γPPN=ω+1ω+2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _{\\,\ ext {PPN}}=\\frac{\\omega +1}{\\omega +2}$$\\end{document}, we obtain the analytical expression γexact=ω+1+(ω+2)Θω+2+(ω+1)Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _{\\,\ ext {exact}}=\\frac{\\omega +1+(\\omega +2)\\Theta }{\\omega +2+(\\omega +1)\\Theta }$$\\end{document} where Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document} is the ratio of the total pressure P‖∗+2P⊥∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{\\parallel }^{*}+2P_{\\perp }^{*}$$\\end{document} and total energy E∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E^{*}$$\\end{document} contained within the star. The dimensionless quantity Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document} participates in γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} due to the scalar degree of freedom of Brans–Dicke gravity. Our non-perturbative formula is valid for all field strengths and types of matter comprising the star. In addition, we establish two new mathematical identities linking the active gravitational mass, the ADM (Arnowitt–Deser–Misner) mass, and the Tolman mass, applicable for Brans–Dicke gravity. We draw four key conclusions:(1) The usual γPPN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _{\\,\ ext {PPN}}$$\\end{document} formula is violated for high-pressure mass sources, such as neutron stars, viz. when Θ≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta \ e 0$$\\end{document}, revealing a limitation of the PPN approximation in Brans–Dicke gravity. (2) The PPN result mainly stems from the assumption of pressureless matter. Even in the weak-field star case, non-zero pressure leads to a violation of the PPN formula for γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}. Conversely, the PPN result is a good approximation for low-pressure matter, i.e. when Θ≈0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta \\approx 0$$\\end{document}, for all field strengths. (3) Observational constraints on γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} set joint bounds on ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} and Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document}, with the latter representing a global characteristic of a mass source. If the equation of state of matter comprising the mass source approaches the ultra-relativistic form, entailing Θ≃1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta \\simeq 1$$\\end{document}, γexact\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _{\\,\ ext {exact}}$$\\end{document} converges to 1 irrespective of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}. More generally, regardless of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}, ultra-relativistic matter tends to suppress the scalar degree of freedom in the exterior vacuum of Brans–Dicke stars, reducing the vacuum to the Schwarzschild solution. (4) In a broader context, by exposing a limitation of the PPN approximation in Brans–Dicke gravity, our findings indicate the significance of considering the interior structure of stars in observational astronomy when testing candidate theories of gravitation that involve additional degrees of freedom besides the metric tensor.

The Brans–Dicke field in non-metricity gravity: cosmological solutions and conformal transformations

We consider the Brans–Dicke theory in non-metricity gravity, which belongs to the family of symmetric teleparallel scalar–tensor theories. Our focus lies in exploring the implications of the conformal transformation, as we derive the conformal equivalent theory in the Einstein frame, distinct from the minimally coupled scalar field theory. The fundamental principle of the conformal transformation suggests the mathematical equivalence of the related theories. However, to thoroughly analyze the impact on physical variables, we investigate the spatially flat Friedmann–Lemaître–Robertson–Walker geometry, defining the connection in the non-coincidence gauge. We construct exact solutions for the cosmological model in one frame and compare the physical properties in the conformal related frame. Surprisingly, we find that the general physical properties of the exact solutions remain invariant under the conformal transformation. Finally, we construct, for the first time, an analytic solution for the symmetric teleparallel scalar–tensor cosmology.

Quantum cosmology in coupled Brans–Dicke gravity: A Noether symmetry analysis

This work deals with a multi-field cosmological model in a spatially flat FLRW spacetime geometry. The usual Brans–Dicke (BD) field and another scalar field are minimally coupled to gravity while they interact with each other through the Kinetic terms. The main aim of this work is to examine whether the model is compatible with cosmic observations. So cosmological solutions are obtained using symmetry analysis only. By imposing Noether Symmetry to the Lagrangian of the system, the potential of the scalar field as well as the coupling function had been determined. The classical solutions are determined after simplifying the Lagrangian using cyclic variables. Finally, Wheeler–DeWitt (WD) equation in quantum cosmology has been formulated and conserved momenta corresponding to Noether symmetry will show the periodic part of the wave function and it helps to have the complete integral for the wave function.

Analytic Solution and Noether Symmetries for the Hyperbolic Inflationary Model in the Jordan Frame

The Noether symmetry analysis is applied for the study of a multifield cosmological model in a spatially flat FLRW background geometry. The gravitational Action Integral consists of two scalar fields, the Brans–Dicke field and a second scalar field minimally coupled to gravity. However, the two scalar fields interact in kinetic terms. This multifield has been found to describe the equivalent of hyperbolic inflation in the Jordan frame. The application of Noether’s theorems constrains the free parameters of the model so that conservation laws exist. We find that the field equations form an integrable dynamical system, and the analytic solution is derived.

Hyperbolic Inflation in the Jordan Frame

We consider a multi-scalar field model in the Jordan frame, which can be seen as a two-scalar field model where the Brans–Dicke field interacts in the kinetic part with the second scalar field. This theory under a conformal transformation reduces to the hyperbolic inflation. We show that scaling solutions and the de Sitter universe are provided by the theory. In the study of asymptotic dynamics, we determine an attractor where all the fluid sources contribute in the cosmological fluid. This attractor is always a spiral, and it can be seen as the analogue of the hyperbolic inflation in the Jordan frame.

A brief note on the limit ω →∞ in Weyl geometrical scalar–tensor theory

We obtain vacuum solutions in the presence of a cosmological constant in the context of the Weyl geometrical scalar–tensor theory. We investigate the limit when [Formula: see text] goes to infinity and show by working out the solutions that in this limit there are some cases in which the scalar field tends to a constant (with the implicit consequence of the geometry becoming Riemannian), although the solutions do not reduce to the corresponding Einstein solutions. We have also extended a previous result, known in the literature, by showing that in the case of vacuum with cosmological constant the field equations of the Weyl geometrical scalar–tensor theory are formally identical to Brans–Dicke field equations, even though these theories are not physically equivalent.

Cosmic acceleration in an extended Brans–Dicke–Higgs theory

ABSTRACT We consider an extended scalar–tensor theory of gravity where the action has two interacting scalar fields, a Brans–Dicke field that makes the effective Newtonian constant a function of coordinates and a Higgs field that has derivative and non-derivative interaction with the lagrangian. There is a non-trivial interaction between the two scalar fields that dictates the dominance of different scalar fields in different era. We investigate if this set-up can describe a late-time cosmic acceleration preceded by a smooth transition from deceleration in recent past. From a cosmological reconstruction technique, we find the scalar profiles as a function of redshift. We find the constraints on the model parameters from a Markov chain Monte Carlo analysis using observational data. Evolution of an effective equation of state, matter density contrast, and thermodynamic equilibrium of our Universe are studied and their significance in comparison with a ΛCDM cosmology is discussed.

Dynamical analysis of Brans–Dicke universe with inverse power-law effective potential

We study Brans–Dicke cosmology with an inverse power-law effective potential. By using dynamical analyses, we search for fixed points corresponding to the radiation-like matter and dark energy-dominated era of our Universe, and the stability of fixed points is also investigated. We find phase space trajectories which are attracted to the stable point of the dark energy-dominated era from unstable fixed points like matter-dominated era of the Universe. The dark energy comes from effective potentials of the Brans–Dicke field, whose variation (related to the time-variation of the gravitational coupling constant) is shown to be in good agreement with observational data.

Whether dark energy can contribute to the treatment and healing of diseases

In studying a five-dimensional universe entangled with Brans–Dicke (BD) field, it is amazingly found that a portion of the dark energy contained in this universe may contribute to the treatment and healing of different diseases and illnesses in human beings. But in such activities, the dark energy, in some cases, might have been transformed into other forms of energy. The reaction between the dark energy and the different kinds of matter contained in this universe is found to possibly have some power to rejuvenate many forms of lives in this cosmos.

Some interactions of spherically symmetric massive scalar field with Brans–Dicke scalar field in Robertson–Walker universe

Here in this work, we investigated the possible cosmological consequences of the interaction of Brans–Dicke scalar field and massive scalar field by considering spherically symmetric Robertson–Walker metric. The present problem can also be treated as an extension work of [K. Priyokumar et al., Interaction of gravitational field and Brans–Dicke field, Res. Astron. Astrophys. 16(4) (2016) 64; K. Priyokumar and M. Dewri, Interaction of electromagnetic field and Brans–Dicke field, Chinease J. Phys. 54 (2016) 845]. The exact solutions of the field equations are obtained with seven different cases. The behavior of the model and their contribution to the process of the evolution are examined in detail from some explicit and reasonable values of free parameter. We also presented the variations of certain physical parameters versus cosmic time graphically to compare our solutions with the present observational findings. When we studied further, it is found that the cosmological term [Formula: see text] takes a great role in the accelerating expansion of our universe when both scalar fields are exponentially increasing functions of time, while the cosmological term will not appear in the case when both the scalar fields are exponentially decreasing functions of time. Also, the scalar field is seen to have a tendency to increase the expansion of the universe, thereby flattening the universe.

Brans–Dicke scalar field cosmological model in Lyra’s geometry with time-dependent deceleration parameter

From the recent observations, it is well known that the expansion rate of our universe varies with time (early decelerating and accelerating in the present epoch) which is an unsolved problem. This motivated to us to consider this paper and so we have developed a new cosmological model in Einstein’s modified gravity theory using two types of modifications: (i) Geometrical modification, in which we have used Lyra’s geometry in the curvature part of the Einstein field equations (EFE) and (ii) Modification in gravity (energy momentum tensor) on right hand side of EFE, as per the Brans–Dicke model. With these two modifications, we have obtained the exact solutions of Einstein Brans–Dicke field equations in Lyra’s geometry for a spatially homogeneous Bianchi type-I space-time with time variable deceleration parameter (DP). We have calculated various physical parameters for the model and found them consistent with recent observations. We have also examined the energy conditions for the model and found them satisfactory. We have found that the scalar field of Brans–Dicke theory behaves like a best fit dark energy candidate in the reference of Lyra’s geometry.

Anisotropic string cosmological model in Brans–Dicke theory of gravitation with time-dependent deceleration parameter

We discuss a spatially homogeneous and anisotropic string cosmological models in the Brans–Dicke theory of gravitation. For a spatially homogeneous metric, it is assumed that the expansion scalar θ is proportional to the shear scalar σ. This condition leads to A = kBm, where k and m are constants. With these assumptions and also assuming a variable scale factor a = a(t), we find solutions of the Brans–Dicke field equations. Various phenomena like the Big Bang, expanding universe, and shift from anisotropy to isotropy are observed in the model. It can also be seen that in early stage of the evolution of the universe, strings dominate over particles, whereas the universe is dominated by massive strings at the late time. Some physical and geometrical behaviors of the models are also discussed and observed to be in good agreement with the recent observations of SNe la supernovae.

The effect of backreaction on inflationary Brans–Dicke cosmology

In this paper, we study the effect of the quantum backreaction on Brans–Dicke cosmology in inflation era. We consider an inflaton field in the [Formula: see text]-dimensional spacetime in the framework of Brans–Dicke model. We use a new notation for the Brans–Dicke field in terms of the dilaton field. Then we obtain the vacuum expectation value of the full energy–momentum tensor using WKB approximation of the mode functions which satisfy the equations of motion. The obtained vacuum expectation values of energy–momentum tensor are divergent. In order to renormalize it, we introduce a constant cut-off [Formula: see text]. The vacuum expectation value of energy–momentum tensor is separated to the UV and IR parts by using [Formula: see text] cut-off. Then, we use the dimensional regularization method to eliminate divergences by introducing a counterterm action. Also, we calculate the IR contribution of the vacuum expectation value of energy–momentum tensor. Thus, we obtain a physically finite result for the quantum energy–momentum tensor. Finally, we find the effect of backreaction on scale factor.

Robertson–Walker model universe interacting with electromagnetic field and Brans–Dicke field in presence of hybrid scale factor

We discuss the Robertson–Walker model universe with a hybrid scale factor for two cases: Flat and Open model interacting with Brans–Dicke field and electromagnetic field. Some exact solutions are obtained and the different characteristics and phenomena of the dark energy contained in it are discussed.

Brans-Dicke cosmology does not have theΛCDMphase as a universal attractor

In this paper we seek for relevant information on the asymptotic cosmological dynamics of the Brans--Dicke theory of gravity for several self-interaction potentials. By means of the simplest tools of the dynamical systems theory, it is shown that the general relativity de Sitter solution is an attractor of the Jordan frame (dilatonic) Brans--Dicke theory only for the exponential potential $U(\vphi)\propto\exp\vphi$, which corresponds to the quadratic potential $V(\phi)\propto\phi^2$ in terms of the original Brans--Dicke field $\phi=\exp\vphi$, or for potentials which asymptote to $\exp\vphi$. At the stable de Sitter critical point, as well as at the stiff-matter equilibrium configurations, the dilaton is necessarily massless. We find bounds on the Brans--Dicke coupling constant $\omega_\textsc{bd}$, which are consistent with well-known results.

Condensation of photons coupled to a Dicke field in an optical microcavity

Motivated by recent experiments reporting Bose-Einstein condensation of light coupled to incoherent dye molecules in a microcavity, we show that due to a dimensionality mismatch between the two-dimensional cavity photons and the three-dimensional arrangement of molecules, the system permits superfluid regimes where the relevant molecular degrees of freedom are collective Dicke states rather than individual excitations. For sufficiently high dye concentration, Dicke states become robust against local decoherence. In the limit when all dye molecules become excited, this system also shows Mott-Hubbard physics, despite the absence of an underlying lattice.

Cylindrically Symmetric and Plane Symmetric Vacuum Cosmological Models in Brans–Dicke Theory

The article presents an exact solution of the vacuum Brans–Dicke (BD) field equations for the metric tensor of a spatially homogeneous and anisotropic cylindrically symmetric and plane symmetric cosmological models. Some physical properties of these models are also discussed. Finally these models have been transformed to the original form (1961) of BD theory.

Existence of naked singularities in the Brans–Dicke theory of gravitation. An analytical and numerical study

Within the framework of the scalar–tensor models of gravitation and by relying on analytical and numerical techniques, we establish the existence of a class of spherically symmetric spacetimes containing a naked singularity. Our result relies on and extends a work by Christodoulou on the existence of naked singularities for the Einstein–scalar field equations. We establish that a key parameter in Christodoulou's construction couples to the Brans–Dicke field and becomes a dynamical variable, which enlarges and modifies the phase space of solutions. We recover analytically many properties first identified by Christodoulou, in particular the loss of regularity (especially at the center), and then investigate numerically the properties of these spacetimes.

Responses of the Brans–Dicke field due to gravitational collapses

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 behaviors during the gravitational collapse and view the energy–momentum tensor components. For the late time behaviors, if the Brans–Dicke coupling is greater (or smaller) than −1.5, the Brans–Dicke field decreases (or increases) during the gravitational collapse. Since the Brans–Dicke field should be relaxed to the asymptotic value with the elapse of time, the final apparent horizon becomes time-like (or space-like). For the dynamical behaviors, we observed the energy–momentum tensors around ω ∼ −1.5. If the Brans–Dicke coupling is greater than −1.5, the Tuu component can be negative at the outside of the black hole. This can allow an instantaneous inflating region during the gravitational collapse. If the Brans–Dicke coupling is less than −1.5, the oscillation of the Tvv component allows the apparent horizon to shrink. This allows a combination that violates weak cosmic censorship. Finally, we discuss the implications of the violation of the null energy condition and weak cosmic censorship.

Interacting holographic dark energy in Brans–Dicke theory

We study cosmological application of interacting holographic energy density in the framework of Brans–Dicke cosmology. We obtain the equation of state and the deceleration parameter of the holographic dark energy in a non-flat universe. As system's IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as L=ar(t). We find that the combination of Brans–Dicke field and holographic dark energy can accommodate wD=−1 crossing for the equation of state of noninteracting holographic dark energy. When an interaction between dark energy and dark matter is taken into account, the transition of wD to phantom regime can be more easily accounted for than when resort to the Einstein field equations is made.