Brans-Dicke Research Articles

Modified-gravity theories with nondynamical background fields

We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{\mu\nu}$ in the literature. An ADM decomposition allows us to project the modified Einstein equations into purely spacelike hypersurfaces, which implies the field equations for the induced dynamical three-metric. We also obtain the Hamilton-Jacobi equations of motion for the canonical variables of the theory based on its Hamiltonian, which was derived in a previous work. The computations show that the dynamical field equations obtained from the Lagrangian and Hamiltonian approaches are consistent with each other. Connections to Brans-Dicke theory and ghost-free massive gravity are established.

Noncompactified Kaluza–Klein Gravity

We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space–Time–Matter theory, or Induced Matter theory, and the reduction procedure used to construct the modified Brans–Dicke theory and the modified Sáez–Ballester theory are briefly explained. Finally, we apply the latter to the Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological models in arbitrary dimensions and analyze the corresponding solutions.

Brans–Dicke Unimodular Gravity

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 remain the same as in the traditional Brans–Dicke theory.

Conceptual design and science cases of a juggled interferometer for gravitational wave detection

The Juggled interferometer (JIFO) is an earth-based gravitational wave detector using repeatedly free-falling test masses. With no worries of seismic noise and suspension thermal noise, the JIFO can have much better sensitivity at lower frequencies than the current earth-based gravitational wave detectors. The data readout method of a JIFO could be challenging if one adopts the fringe-locking method. We present a phase reconstruction method in this paper by building up a complex function which has a fringe-independent signal-to-noise ratio. Considering the displacement noise budget of the Einstein Telescope (ET), we show that the juggled test masses significantly improve the sensitivity at 0.1-2.5$\,$Hz even with discontinuous data. The science cases brought with the improved sensitivity would include detecting quasi-normal modes of black holes with $10^4-10^5\,M_{\odot}$, testing Brans-Dicke theory with black-hole and neutron-star inspirals, and detecting primordial-black-hole-related gravitational waves.

Searches for Gravitational Waves from Known Pulsars at Two Harmonics in the Second and Third LIGO-Virgo Observing Runs

We present a targeted search for continuous gravitational waves (GWs) from 236 pulsars using data from the third observing run of LIGO and Virgo (O3) combined with data from the second observing run (O2). Searches were for emission from the l = m = 2 mass quadrupole mode with a frequency at only twice the pulsar rotation frequency (single harmonic) and the l = 2, m = 1, 2 modes with a frequency of both once and twice the rotation frequency (dual harmonic). No evidence of GWs was found, so we present 95% credible upper limits on the strain amplitudes h 0 for the single-harmonic search along with limits on the pulsars’ mass quadrupole moments Q 22 and ellipticities ε. Of the pulsars studied, 23 have strain amplitudes that are lower than the limits calculated from their electromagnetically measured spin-down rates. These pulsars include the millisecond pulsars J0437−4715 and J0711−6830, which have spin-down ratios of 0.87 and 0.57, respectively. For nine pulsars, their spin-down limits have been surpassed for the first time. For the Crab and Vela pulsars, our limits are factors of ∼100 and ∼20 more constraining than their spin-down limits, respectively. For the dual-harmonic searches, new limits are placed on the strain amplitudes C 21 and C 22. For 23 pulsars, we also present limits on the emission amplitude assuming dipole radiation as predicted by Brans-Dicke theory.

Kaniadakis holographic dark energy in Brans–Dicke cosmology

By using the holographic hypothesis and Kaniadakis generalized entropy, which is based on relativistic statistical theory and modified Boltzmann–Gibbs entropy, we build Kaniadakis holographic dark energy (DE) model in the Brans–Dicke framework. We derive cosmological parameters of the Kaniadakis holographic DE model, with IR cutoff as the Hubble horizon, in order to investigate its cosmological consequences. Our study shows that even in the absence of an interaction between the dark sectors of the cosmos, the Kaniadakis holographic dark energy model with the Hubble radius as IR cutoff can explain the present accelerated phase of the universe expansion in the Brans–Dicke theory. The stability of the model, using the squared of sound speed, has been checked and it is found that the model is unstable in non-interacting case and can be stable for some range of model parameters within the interacting case.

Peculiar thermal states in the first-order thermodynamics of gravity

In the context of the recently proposed first-order thermodynamics of scalar-tensor gravity, we discuss the possibility of zero-temperature states of equilibrium other than Einstein gravity, including pathological Brans-Dicke theory, Palatini $f(R)$ gravity, and cuscuton gravity, all with nondynamical scalar fields. The formalism is extended to Nordstr\"om gravity, which contains only a scalar degree of freedom and has negative temperature relative to general relativity.

Energy conditions in a modified Brans-Dicke theory

We consider a modified version of Brans-Dicke theory (MBDT) in four dimensions (4D) obtained by applying the induced matter method of Wesson to a 5D generalized Brans-Dicke theory. In 5D the model consists of pure vacuum, with no self-interacting potential, except for a scalar field. Following Wesson’s protocol, we group geometric terms in the 5D Einstein tensor arising from the extra dimension, move them to the other side of the generalized field equations, and identify them as the energy-momentum of the induced matter in 4D. Thus the extra dimension in 5D leads naturally to an effective matter field in 4D. Constraining the 5D geometry to be a generalization of the anisotropic Bianchi type I universe model first studied by Kasner, we derive the induced energy-momentum in MBDT and apply it to the investigation of energy conditions. The specified induced energy-momentum of that MBDT model consists of the energy density and directional pressure which indicate the anisotropy of the universe. We discuss the energy conditions and their bounds in the MBDT with such an induced imperfect fluid, with an eye toward a realistic model of the present-day universe, and consider the large-scale behavior of that spatially homogeneous and anisotropic model. We discuss how the energy conditions would be satisfied or violated in the context of MBDT, with the aim of providing a feasible description of the universe in the current era.

Binary X-ray Sources in Massive Brans–Dicke Gravity

This study focuses on the X-ray emission of low-mass black hole binaries in massive Brans–Dicke gravity. First, we compute the accretion disk with the well-known Shakura–Sunyaev model for an optically thick, cool, and geometrically thin disk. Moreover, we assume that the gravitational field generated by the stellar-mass black hole is an analogue of the Schwarzschild space-time of Einstein’s theory in massive Brans–Dicke gravity. We compute the most relevant quantities of interest, i.e., (i) the radial velocity, (ii) the energy and surface density, and (iii) the pressure as a function entirely of the radial coordinate. We also compute the soft spectral component of the X-ray emission produced by the disk. Furthermore, we investigate in detail how the mass of the scalar field modifies the properties of the binary as described by the more standard Schwarzschild solution.

Screening mechanism and late-time cosmology: Role of a Chameleon–Brans–Dicke scalar field

ABSTRACT We discuss a way in which the geometric scalar field in a Brans–Dicke (BD) theory can evade local astronomical tests and act as a driver of the late-time cosmic acceleration. This requires a self-interaction of the BD scalar as well as an interaction with ordinary matter. The scalar field in this construct acquires a density-dependent effective mass much like a Chameleon field. We discuss the viability of this setup in the context of Equivalence Principle, Fifth Force, and Solar System tests. The cosmological consistency is adjudged in comparison with observational data from recalibrated light curves of type Ia supernova (JLA), the Hubble parameter measurements (OHD) and the Baryon Acoustic Oscillation (BAO). We deduct that the astrophysical constraints indeed favour the existence of a mild scalar-matter interaction in the Jordan Frame.

Analysis of generalized ghost dark energy and new holographic dark energy in Chameleon Brans–Dicke theory

In this work, we discuss the stability analysis of generalized ghost dark energy (GGDE) and new holographic dark energy (NHDE) in the framework of Chameleon Brans–Dicke (CBD) gravity. The adiabatic squared sound speed [Formula: see text] plays a crucial role to analyze the stability of the models. We know that the models are stable if [Formula: see text] and unstable if [Formula: see text]. We study the interacting and noninteracting versions of GGDE and NHDE with dark matter in CBD model in a nonflat FLRW universe. We also try to show that in all cases of investigation, the models are classically stable with suitable choices of parameters. Finally, we analyze the perturbative analysis for both GGDE and NHDE models in the background of CBD gravity.

Stealth metastable state of scalar-tensor thermodynamics

We investigate a puzzle in the recent thermodynamics of scalar-tensor gravity, in which general relativity is a zero-temperature state of equilibrium and scalar-tensor gravity is the non-equilibrium configuration of an effective dissipative fluid. A stealth solution of Brans-Dicke gravity with constant positive temperature is shown to be analogous to a metastable state for the effective fluid and to suffer from an instability. The stability analysis employs a version of the Bardeen-Ellis-Bruni-Hwang gauge-invariant formalism for cosmological perturbations adapted to modified gravity. The metastable state is destroyed by tensor perturbations.

Dark matter and dark energy from a Kaluza–Klein inspired Brans–Dicke gravity with barotropic fluid

We study the Kaluza–Klein inspired Brans–Dicke model with barotropic matter. Following from our previous work, the traditional Kaluza–Klein gravity action is introduced with an additional scalar field and 2 gauge fields. The compactification process results in a Brans–Dicke model with a dilaton coupled to the tower of scalar fields whereas a gauge field from 5-dimensional metric forms a set of mutually orthogonal vectors with 2 additional gauge fields. The barotropic matter is then introduced to complete a realistic set up. To demonstrate the analytical solutions of the model, we consider the case in which only 2 lowest modes becoming relevant for physics at low scale. After derivation, equations of motion and Einstein field equations form a set of autonomous system. The dynamical system is analysed to obtain various critical points. Interestingly, by only inclusion of barotropic matter, the model provides us the critical points which capable of determining the presences of dark matter, dark energy and phantom dark energy.

Constraining Brans–Dicke Cosmology with the CSST Galaxy Clustering Spectroscopic Survey

The Brans–Dicke (BD) theory is the simplest Scalar-Tensor theory of gravity, which can be considered as a candidate of modified Einstein’s theory of general relativity. In this work, we forecast the constraints on BD theory in the CSST galaxy clustering spectroscopic survey with a magnitude limit ∼23 AB mag for point-source 5σ detection. We generate mock data based on the zCOSMOS catalog and consider the observational and instrumental effects of the CSST spectroscopic survey. We predict galaxy power spectra in the BD theory from z = 0 to 1.5, and the galaxy bias and other systematical parameters are also included. The Markov Chain Monte Carlo technique is employed to find the best-fits and probability distributions of the cosmological and systematical parameters. A BD parameter ζ is introduced, which satisfies . We find that the CSST spectroscopic galaxy clustering survey can give ∣ζ∣ < 10−2, or equivalently and , under the assumption ζ = 0. These constraints are almost at the same order of magnitude compared to the joint constraints using the current cosmic microwave background, baryon acoustic oscillations and Type Ia supernova data, indicating that the CSST galaxy clustering spectroscopic survey would be powerful for constraining the BD theory and other modified gravity theories.

Shadows in conformally related gravity theories

Null geodesics are invariant under a conformal transformation, and thus it might seem natural to assume that the observables corresponding to the shadow of a space-time are also conformally invariant. Here, we argue instead, that since the Arnowitt-Deser-Misner mass and the active gravitational mass of an asymptotically flat space-time are not, in general, invariant under such conformal transformations, the shadow radius for photon motion in a space-time would be quantitatively different, when viewed from two different conformally related frames, although the expression for the shadow radius is similar. We then use this fact to propose a novel method to constrain the relevant parameters in a gravity theory conformally related to general relativity. As examples of our method, we constrain the parameter space in Brans-Dicke theory, and a class of brane-world gravity models, by using the recent observational data of M87⁎ by the Event Horizon Telescope.

A Swinging Rod in Brans‐Dicke Theory

AbstractThis article presents the calculation of gravitational radiation from an oscillating rod in Brans–Dicke (BD) theory. Here only the selected formulae is shown and is applied to a toy problem without any rigorous derivation. First, the explicit expressions for the polarizations are calculated and then the power radiated away in gravitational waves (GWs) is obtained. This problem is motivated by the famous Eddington's spinning rod.

Study of axially symmetric viscous Ricci dark energy model in Brans–Dicke theory

In this paper, we have investigated axially symmetric and anisotropic space–time filled with viscous Ricci dark energy and pressure-less dark matter in the frame-work of Brans–Dicke(BD) theory of gravitation. To solve the field equations, we use the following conditions: (i) the relationship between metric potentials which is obtained from the condition that shear scalar of the model is directly proportional to the expansion scalar, (ii) the average scale factor varies with time as a(t)=[sinh(αt)]1k, and (iii) the bulk viscous coefficient (ξ) as ξ=ξ0+ξ1h+ξ2h′′, where ξ0, ξ1 and ξ2 are constants and h=HH0. We have studied the cosmological parameters, like bulk viscosity coefficient (ξ), effective equation of state (ωeft), deceleration (q), Om diagnostic and cosmological planes like state-finder diagnostics {r,s} and {r,q} planes. And also, we have analyzed the physical behavior of these parameters through pictorial representation. The deceleration and effective equation of state parameters are very close to recent observational data in our model.

Jordan and Einstein frames from the perspective of ω=−3/2 Hamiltonian Brans-Dicke theory

We carefully perform a Hamiltonian Dirac's constraint analysis of the $\ensuremath{\omega}=\ensuremath{-}\frac{3}{2}$ Brans-Dicke theory with the Gibbons-Hawking-York boundary term. The Poisson brackets are computed via functional derivatives. After a brief summary of the results for the $\ensuremath{\omega}\ensuremath{\ne}\ensuremath{-}\frac{3}{2}$ case [G. Gionti S. J., Canonical analysis of Brans-Dicke theory addresses Hamiltonian inequivalence between the Jordan and Einstein frames, Phys. Rev. D 103, 024022 (2021)] we derive all Hamiltonian Dirac's constraints and constraint algebra in both the Jordan and the Einstein frames. Confronting and contrasting Dirac's constraint algebra in both frames, it is shown that they are not equivalent. This highlights that the transformations from the Jordan to the Einstein frames are not Hamiltonian canonical transformations.

FRW cosmological models with Barrow holographic dark energy in Brans–Dicke theory

In this paper, we have generalized the behaviors of transit cosmological model under the observational data with Barrow holographic dark energy. We consider the scale factor field as [Formula: see text] to get exact solutions for the field equations in a non-flat FRW universe in Brans–Dicke theory. The values of the model parameters [Formula: see text] and [Formula: see text] are obtained by best fitting of 46 observational Hubble data (OHD) points in the range [Formula: see text]. The derived model exhibits a transition scenario for open, flat and closed universe. The EoS parameter shows a quintom-like behavior, lies both quintessence ([Formula: see text]) and phantom ([Formula: see text]) regions and crosses the phantom divide. The matter and dark energy density parameters [Formula: see text], scalar field [Formula: see text] and other cosmological parameters provide the results consistent with the recent observational datasets. Some other physical and geometrical behaviors of BHDE are also described and the satisfactory behaviors are found with current observations (OHD+JLA).

Conserved charges in Chern-Simons modified theory and memory effects

In this work, conserved charges and fluxes at the future null infinity are determined in the asymptotically flat spacetime for Chern-Simons modified gravity. The flux-balance laws are used to constrain the memory effects. For tensor memories, the Penrose's conformal completion method is used to analyze the asymptotic structures and asymptotic symmetries, and then, conserved charges for the Bondi-Metzner-Sachs algebra are constructed with the Wald-Zoupas formalism. These charges take very similar forms to those in Brans-Dicke theory. For the scalar memory, Chern-Simons modified gravity is rewritten in the first-order formalism, and the scalar field is replaced by a 2-form field dual to it. With this dual formalism, the scalar memory is described by the vacuum transition induced by the large gauge transformation of the 2-form field.