Brans-Dicke Research Articles

Generalized ghost dark energy model in Brans–Dicke theory with logarithmic scalar field

We study generalized ghost dark energy model in Brans–Dicke theory within the framework of flat Friedmann–Lemaitre–Robertson–Walker Universe. We assume the well-motivated logarithmic form of Brans–Dicke scalar field in terms of the scale factor to find the observational parameters such as equation of state parameter [Formula: see text] and deceleration parameter q. It is observed that the equation of state parameter crosses the phantom divide line [Formula: see text] for a suitable range of model parameters. We observe that the deceleration parameter is time-dependent which shows the recent phase transition from decelerated to accelerated expansion of the Universe. Moreover, the model shows that the Universe will go through two future phase transitions, recent accelerated expansion to decelerated expansion and again decelerated expansion to accelerated expansion. We have also plotted the trajectories of the model in the [Formula: see text] plane for different values of parameters and explored the freezing and thawing regions. Further, we apply the sound squared speed method to check the stability of the model and found that the model is stable for suitable range of parameters.

Bouncing and collapsing universes dual to late-time cosmological models

We use the Jordan frame–Einstein frame correspondence to explore dual universes with contrasting cosmological evolutions. We study the mapping between Einstein and Jordan frames where the Einstein frame universe describes the late-time evolution of the physical universe, which is driven by dark energy and non-relativistic matter. The Brans–Dicke theory of gravity is considered to be the dual scalar–tensor theory in the Jordan frame. We show that an Einstein frame universe, with cosmological evolution of the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model, always corresponds to a bouncing Jordan frame universe governed by a Brans–Dicke theory. On the other hand, quintessence models of dark energy with non-relativistic matter component are shown to be always dual to a Brans–Dicke Jordan frame with a turn-around, i.e., a bounce or a collapse. The evolution of the equation of state of the quintessence field determines whether the turn-around is a bounce or a collapse. The point of the Jordan frame turn-around for all the cases can be tuned anywhere by choosing an appropriate Brans–Dicke parameter. This essentially leads to alternative descriptions of the late-time evolution of the physical universe, in terms of bouncing or collapsing Brans–Dicke universes in the Jordan frame. Therefore, the effect of dark energy can equivalently be seen as collapse of space in a conformally connected universe. We further study the stability of such conformal maps against linear perturbations. The effective bouncing and collapsing descriptions of the current accelerating universe may have interesting implications for the evolutions of perturbations and quantum fluctuations in the cosmological background.

Erratum — Static spherically symmetric black holes of Brans–Dicke theory of gravity

Erratum — Static spherically symmetric black holes of Brans–Dicke theory of gravity

Cosmic Aspects of Sharma-Mittal Holographic Dark Energy Model in Brans-Dicke Theory of Gravity

We investigate the cosmological scenario involving spatially homogeneous and anisotropic Bianchi type-V I0 space-time in the context of the Sharma-Mittal holographic dark energy model within the framework of Brans-Dicke’s theory of gravitation. In order to achieve this objective, the Hubble, deceleration, equation-of-state parameters have been discussed. The deceleration parameter (q) is used to measure the pace at which the expansion of the universe is accelerating. The equation-of-state parameter (ωsmhde) characterizes the quintessence and vacuum areas of the universe. All the parameters demonstrate consistent behaviour following the Planck 2018 data. We assess the dynamical stability by defining the squared speed of sound and examining its behaviour. In addition, the energy conditions and the variation of ωsmhde and ω′smhde in the model indicate the present accelerating expansion of the universe.

Gravitational collapse without singularity formation in Brans–Dicke theory

Gravitational collapse without singularity formation in Brans–Dicke theory

Cosmological consequences of Brans–Dicke theory in 4D from 5D scalar-vacuum

We study 5D Brans–Dicke theory in the framework of (gravitational) baryogenesis and primordial light element formation. Such a model is able to explain the present cosmic accelerated expansion without recurring to matter fields in 5D or dark energy in 4D. In fact, the 5D to 4D reduction arises a space-matter tensor of geometrical origin that plays the role of a new ingredient on-shell. For an isotropic and homogeneous Universe, the cosmological equations admit a power-law solution of the scale factor, a(t)∼tα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a(t)\\sim t^\\alpha$$\\end{document}, we constrain the exponential factor α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} by using the present bounds on the matter–antimatter asymmetry in the Universe and Big Bang Nucleosynthesis. A possible connection with dark matter relic abundance is also discussed.

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.

Bayesian test of Brans–Dicke theories with planetary ephemerides: Investigating the strong equivalence principle

Aims. We are testing the Brans–Dicke class of scalar tensor theories with planetary ephemerides. Methods. In this work, we apply our recently proposed Bayesian methodology to the Brans–Dicke case, with an emphasis on the issue of the strong equivalence principle (SEP). Results. We use an MCMC approach coupled to full, consistent planetary ephemeris construction (from point-mass body integration to observational fit) and compare the posterior distributions obtained with and without the introduction of potential violations of the SEP. Conclusions. We observe a shift in the confidence levels of the posteriors obtained. We interpret this shift as marginal evidence that the effect of violation of the SEP can no longer be assumed to be negligible in planetary ephemerides with the current data. We also notably report that the constraint on the Brans–Dicke parameter with planetary ephemerides is getting closer to the figure reported from the Cassini spacecraft alone, and also to the constraints from pulsars. We anticipate that data from future spacecraft missions, such as BepiColombo, will significantly enhance the constraints based on planetary ephemerides.

Equations of electrodynamics in the context of the Brans-Dicke theory

Equations of electrodynamics in the context of the Brans-Dicke theory

Recent acceleration and future deceleration in Brans–Dicke theory

Recent acceleration and future deceleration in Brans–Dicke theory

Running vacuum in Brans & Dicke theory: A possible cure for the [formula omitted] and [formula omitted] tensions

Extensions of the gravitational framework of Brans & Dicke (BD) are studied by considering two different scenarios: (i) ‘BD-ΛCDM’, in which a rigid cosmological constant, Λ, is included, thus constituting a BD version of the vanilla concordance ΛCDM model (the current standard model of cosmology with flat three-dimensional geometry), and (ii) ‘BD-RVM’, a generalization of (i) in which the vacuum energy density (VED), ρvac, is a running quantity evolving with the square of the Hubble rate: δρvac(H)∝νmPl2(H2−H02) (with |ν|≪1 and H0 being the present value of the Hubble rate). This dynamical scenario is motivated by recent studies of quantum field theory (QFT) in curved spacetime, which lead to the running vacuum model (RVM). In both cases, rigid or running ρvac, the GR limit can be recovered smoothly. We solve the background as well as the perturbation equations for each cosmological model and test their performance against the modern wealth of cosmological data, namely a compilation of the latest SNIa+H(z)+BAO+LSS+CMB observations. We utilize the AIC and DIC statistical information criteria in order to determine if they can fit better the observations than the concordance model. The two BD extensions are tested by considering three different datasets. According to the AIC and DIC criteria, both BD extensions (i) and (ii) are competitive, but the second one (the BD-RVM scenario) is particularly favored when it is compared with the vanilla model. This fact may indicate that the current observations favor a mild dynamical evolution of the Newtonian coupling GN as well as of the VED. While further studies will be necessary, the results presented here suggest that the Brans & Dicke theory with running vacuum could have the potential to alleviate the two tensions at the same time.

Cosmological Model with Cosmic Transit Behavior in Brans-Dicke Theory

Cosmological Model with Cosmic Transit Behavior in Brans-Dicke Theory

Gravitational decoupling of anisotropic stars in the Brans–Dicke theory

Anisotropic spherically symmetric solutions within the framework of the Brans–Dicke theory are uncovered through a unique gravitational decoupling approach involving a minimal geometric transformation. This transformation effectively divides the Einstein field equations into two separate systems, resulting in the alteration of the radial metric component. The first system encompasses the influence of the seed source, derived from the metric functions of the isotropic Tolman IV solution. Meanwhile, the anisotropic source is subjected to two specific constraints in order to address the second system. By employing matching conditions to determine the unknown constants at the boundary of the stellar object, a comprehensive examination of the internal structure of stellar systems ensues. This investigation delves into the impact of the decoupling parameter, the Brans–Dicke parameters, and a scalar field on the structural characteristics of anisotropic spherically symmetric spacetimes, all while considering the strong energy conditions.

Closed Timelike Curves Induced by a Buchdahl-Inspired Vacuum Spacetime in R2 Gravity

The recently obtained special Buchdahl-inspired metric Phys. Rev. D 107, 104008 (2023) describes asymptotically flat spacetimes in pure Ricci-squared gravity. The metric depends on a new (Buchdahl) parameter k˜ of higher-derivative characteristic, and reduces to the Schwarzschild metric, for k˜=0. For the case k˜∈(−1,0), it was shown that it describes a traversable Morris–Thorne–Buchdahl (MTB) wormhole Eur. Phys. J. C 83, 626 (2023), where the weak energy condition is formally violated. In this paper, we briefly review the special Buchdahl-inspired metric, with focuses on the construction of the Kruskal–Szekeres (KS) diagram and the situation for a wormhole to emerge. Interestingly, the MTB wormhole structure appears to permit the formation of closed timelike curves (CTCs). More specifically, a CTC straddles the throat, comprising of two segments positioned in opposite quadrants of the KS diagram. The closed timelike loop thus passes through the wormhole throat twice, causing two reversals in the time direction experienced by the (timelike) traveller on the CTC. The key to constructing a CTC lies in identifying any given pair of antipodal points (T,X) and (−T,−X) on the wormhole throat in the KS diagram as corresponding to the same spacetime event. It is interesting to note that the Campanelli–Lousto metric in Brans–Dicke gravity is known to support two-way traversable wormholes, and the formation of the CTCs presented herein is equally applicable to the Campanelli–Lousto solution.

Thermodynamics of higher-dimensional Brans-Dicke black holes in the presence of a conformal-invariant field inspired by power-Maxwell electrodynamics

Abstract By use of the conformal transformations, in addition to translating the Brans-Dicke (BD) action to the Einstein frame (EF), we introduce an electromagnetic Lagrangian which preserves conformal invariance. We solve the EF field equations, which mathematically are confronted with the problem of indeterminacy, by use of an exponential ansatz function. When the self-interacting potential is absent or is taken constant in the BD action, the exact solution of this theory is just that of Einstein-conformal-invariant theory with a trivial scalar field. This is higher-dimensional (HD) analogues of the same considered in [1]. The EF general solution admits two classes of black holes (BHs) with non-flat and non-AdS asymptotic behavior which can produce extreme and multi-horizon ones. We obtain the exact solutions of BD-conformal-invariant theory, by applying inverse conformal transformations, which show two classes of extreme and multi-horizon BHs too. Based on the fact that thermodynamic quantities remain unchanged under conformal transformations, we show that the first law of BH thermodynamics is valid in the Jordan frame (JF). We analyze thermal stability of the HD BD-conformal-invariant BHs by use of the canonical ensemble method.

Static spherically symmetric black holes of Brans–Dicke theory of gravity

This paper investigates the static spherically symmetric vacuum solutions of Brans–Dicke Theory of Gravity. In this paper, we systematically derive the static spherically symmetric solutions by starting with the general static spherically symmetric anzats, discovering the nonzero Christoffel symbols, nonzero Ricci tensor components and the Ricci Scalar. These results allow us to rewrite the four Brans–Dicke gravitational field equations explicitly in terms of the metric components, the scalar field and its scalar potential. This paper systematically explains and shows how to modify these linear second-order ordinary differential equations in order to be able to find the solution of the scalar field, the metric components and the scalar potential analytically. We successfully find the most general solution of the static spherically symmetric vacuum solutions of Brans–Dicke gravity and the well-known Schwarzschild solution is recovered as the simplest solution.

AdS waves in Brans-Dicke theory

AdS waves in Brans-Dicke theory

On the equivalence between theories and Einstein gravity

In this brief note we present a somewhat trivial result. Namely, we show that perturbative off-shell f(R)-theory is equivalent to Einstein gravity, as well as to the Brans–Dicke theory and the Einstein scalar field model. We also discuss possible generalization of this result to higher-order gravitational field models.

An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory

In this study, the homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I universe filled with the bulk viscous and the string cloud matter has been investigated in the Brans-Dicke (BD) scalar-tensor theory. The modified Einstein field equations of the constructed model have been solved by using the relation of the scale factors $A=B^m$ and considering the deceleration parameter to be $q=m-1$. It is found that the string does not survive for the model due to the obtained zero string energy density ($\rho_s=0$) and agrees with some studies in recent years. Moreover, it is possible to say that string matter may be turned into phantom energy over time, depending on the obtained negative rest energy density of the matter. When BD scalar field $\Phi$ is assumed constant, the attained solutions are reduced to General Relativity (GR) solutions for the static vacuum. Thus, the constructed model has not allowed the reduction of the BD solutions to GR solutions, including the matter distributions. In addition, some expansion models for choosing a value of constant $m$ have been obtained and provided. All the results have been analyzed in detail.

A Study of Evolution of Cosmological Parameters Based on a Dark Energy Model in the Framework of Brans-Dicke Gravity

The objective of the present study is to find the characteristics of evolution of a homogeneous and isotropic universe in the framework of Brans-Dicke (BD) theory of gravity. FLRW space-time, with zero spatial curvature, has been used to obtain BD field equations. Scale factor and Hubble parameter have been obtained from an ansatz for the deceleration parameter, assumed on the basis of its property of signature flip indicating a change of phase from deceleration to acceleration. Validation of the model has been achieved by a suitable parametrization of that ansatz. Expressions for energy density, pressure, equation of state (EoS) parameter, cosmological constant, gravitational constant have been derived and depicted graphically. The gravitational constant is found to decrease with time at a gradually decreasing rate. The Hubble parameter, deceleration parameter and energy density decrease with time, which is in agreement with many other studies. The value of the EoS parameter at the present epoch is negative, and it becomes more negative with time. The cosmological constant increases very rapidly in the early universe from negative to smaller negative values, becoming positive finally, with a much slower change thereafter. A cosmographic and a geometrical analysis have been carried out. It is observed that a gradual transition takes place from a regime of quintessence to phantom dark energy. An important finding of this study is that the signature flip of the deceleration parameter takes place almost simultaneously with the signature flip of the cosmological constant, implying a connection between accelerated expansion and dark energy, which is represented here by the cosmological constant. Unlike the common practice of using arbitrary units, proper SI units for all measurable quantities have been used. This theoretical investigation provides the reader with a simple method to formulate models in the framework of BD theory.