Brans-Dicke Research Articles

Violation of the equivalence principle in curvature-based extended gravity at finite temperature

We review the possible violation of the Equivalence Principle at finite temperature [Formula: see text] in the framework of curvature-based Extended Theories of Gravity. Specifically, we first show how it is possible to derive Equivalence Principle violation from Quantum Field Theory at [Formula: see text]. Subsequently, we exhibit how this result can be precisely recovered by following an alternative path that envisages the employment of generalized Einstein equations with a temperature-dependent energy-momentum tensor. Finally, we adopt the latter formalism in the context of some Extended Gravity models to quantify the amount of Equivalence Principle violation. Specifically, Brans–Dicke Theory, Standard Model Extension and Conformal Gravity are considered in detail.

Big Rip Scenario in Brans-Dicke Theory

In this work, we present a Big Rip scenario within the framework of the generalized Brans-Dicke (GBD) theory. In the GBD theory, we consider an evolving BD parameter along with a self-interacting potential. An anisotropic background is considered to have a more general view of the cosmic expansion. The GBD theory with a cosmological constant is presented as an effective cosmic fluid within general relativity which favours a phantom field dominated phase. The model parameters are constrained so that the model provides reasonable estimates of the Hubble parameter and other recent observational aspects at the present epoch. The dynamical aspects of the BD parameter and the BD scalar field have been analysed. It is found that the present model witnesses a finite time doomsday at a time of tBR≃16.14Gyr, and for this scenario, the model requires a large negative value of the Brans-Dicke parameter.

Isotropization and complexity of decoupled solutions in self-interacting Brans–Dicke gravity

The aim of this work is to formulate two new solutions by decoupling the field equations via a minimal geometric deformation in the context of self-interacting Brans–Dicke gravity. We introduce an extra source in the anisotropic fluid distribution to generate new analogs of existing solutions. The radial metric function is transformed to decouple the field equations into two sets such that each array corresponds to one source only. The system corresponding to the original matter distribution is specified by metric functions of well-behaved solutions. On the other hand, the second set is closed by imposing constraints on the additional matter source. For this purpose, we have applied the isotropization condition as well as vanishing complexity condition on the new source. Smooth matching of interior and exterior spacetimes at the junction provides values of the unknown constants. Interesting physical features of corresponding models are checked by employing the mass and radius of the star PSR J1614-2230. It is concluded that both extensions yield viable and stable models for certain values of the decoupling parameter.

Wave optics and weak gravitational lensing of lights from spherically symmetric static scalar vector tensor Brans Dicke wormholes

This paper has three parts. In first step we use modified scalar tensor vector Brans Dicke gravity \cite{GH0} to obtain metric solution of a spherically symmetric static black hole via perturbation method which asymptotically behaves as modified Schwarzschild de Sitter black hole in weak field limits. Corrections on the line element with respect to the point mass Schwarzschild de Sitter black hole are two parts: power law function for black hole mass instead of point mass and additional logarithmic metric potential which they are produced from effects of interacting timelike dynamical vector fields. Second part of the paper is dedicated to review Fresnel-Kirchhoff diffraction theory for massless scalar field instead of the vector electromagnetic waves. In third part of the work we consider the obtained black hole metric to be lens and we study weak gravitational lensing of moving light originated from point star. Production of stationary images is investigated via both interference of waves and geometric optics approaches. At last we compare results of these approaches and give some outlooks.

Geometrical Diagnostics for Modified Gravitational Theory with the Different Formalisms

Geometrical diagnostic methods were often applied to distinguish the gravitational models. But it is scarce to investigate the differences between the different formalisms of modified gravitational theories (e.g. the metric formalism and the Palatini formalism). In this paper, we discriminate the gravitational theory with the different formalisms by using the geometrical diagnostic methods. For a considered modified theory of gravity (e.g. the f(R) theory or GBD theory), we can see that the difference between the two formalisms is remarkable according to the diagnostic results. And relative to the ΛCDM model, there are more deviations in metric formalism than those in Palatini formalism, according to the {r, s} diagnostic. Given that the GBD (generalized Brans-Dicke theory) is a time-variable Newton gravitational constant (VG) theory, the differences between the VG theory and the constant-G theory are studied. It indicates that the variation of Newton’s gravitational constant could induce notable effects on geometrical quantities (e.g. r, s and q) in both metric formalism and Palatini formalism.

Jordan and Einstein Frames Hamiltonian Analysis for FLRW Brans-Dicke Theory

We analyze the Hamiltonian equivalence between Jordan and Einstein frames considering a mini-superspace model of the flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe in the Brans–Dicke theory. Hamiltonian equations of motion are derived in the Jordan, Einstein, and anti-gravity (or anti-Newtonian) frames. We show that, when applying the Weyl (conformal) transformations to the equations of motion in the Einstein frame, we did not obtain the equations of motion in the Jordan frame. Vice-versa, we re-obtain the equations of motion in the Jordan frame by applying the anti-gravity inverse transformation to the equations of motion in the anti-gravity frame.

Bound on the rate of Bondi mass loss

To ensure the light (emitted far away from the source of gravity) can arrive at the null infinity of an asymptotically flat spacetime, it is shown that the rate of Bondi mass aspect has to satisfy some conditions. In Einstein gravity theory, we find the sufficient condition implies a bound on the Bondi mass $m$, i.e., $|\dot{m}|\leqslant 0.3820~c^3/G$. This provides a new perspective on Dyson's maximum luminosity. However, in Brans-Dicke theory, the sufficient condition depends on the behavior of the radiation field of the scalar. Specifically, the photons can escape to the null infinity when the scalar gravitational radiation is not too large and the mass loss is not too fast.

Gravitational-wave memory effects in Brans-Dicke theory: Waveforms and effects in the post-Newtonian approximation

Gravitational-wave (GW) memory effects produce permanent shifts in the GW strain and its time integrals after the passage of a burst of GWs. Their presence is closely tied to symmetries of asymptotically flat spacetimes and fluxes of conserved charges conjugate to these symmetries. While the phenomenology of GW memory effects is well understood in general relativity (GR), it is less well understood in the many modifications to GR. We recently computed asymptotically flat solutions, symmetries, conserved quantities, and GW memory effects in one such modified theory: Brans-Dicke theory. In this paper, we apply our results from this earlier work to compute the GW memories from compact binaries in the post-Newtonian (PN) approximation. In addition to taking the PN limit of these effects, we work in the approximation that the energy and angular momentum losses through scalar radiation are small compared to the energy and angular momentum losses through (tensor) GWs. We focus on the tensor (as opposed to scalar) GW memory effect, which we compute through Newtonian order, and the small differences induced by scalar radiation at this order. Specifically, we compute the nonlinear parts of the tensor displacement and spin GW memory effects produced during the inspiral of quasicircular, nonprecessing binaries in Brans-Dicke theory. Because the energy radiated through the scalar dipole moment appears as a -1 PN order-effect, then in this approximation, the displacement memory has a logarithmic dependence on the PN parameter and the spin memory has a relative -1 PN-order correction; these corrections are ultimately small because they are related to the total energy and angular momentum radiated in the scalar field, respectively. At Newtonian order, the scalar radiation also gives rise to a sky pattern of the memory effect around an isolated source that differs from that of the memory effect in GR.

Constraining Scalar-tensor Theories Using Neutron Star–Black Hole Gravitational Wave Events

Abstract With the continuous upgrade of detectors, greater numbers of gravitational wave (GW) events have been captured by the LIGO Scientific Collaboration and Virgo Collaboration (LVC), which offer a new avenue to test general relativity and explore the nature of gravity. Although various model-independent tests have been performed by LVC in previous works, it is still interesting to ask what constraints can be placed on specific models by current GW observations. In this work, we focus on three models of scalar-tensor theories, the Brans–Dicke theory (BD), the theory with scalarization phenomena proposed by Damour and Esposito-Farèse (DEF), and screened modified gravity (SMG). Of the four possible neutron star–black hole events that have occurred so far, we use two of them to place constraints. The other two are excluded in this work because of possible unphysical deviations. We consider the inspiral range with the cutoff frequency at the innermost stable circular orbit and add a modification of dipole radiation into the waveform template. The scalar charges of neutron stars in the dipole term are derived by solving the Tolman–Oppenheimer–Volkoff equations for different equations of state. The constraints are obtained by performing the full Bayesian inference with the help of the open source software Bilby. The results show that the constraints given by GWs are comparable to those given by pulsar timing experiments for DEF theory, but are not competitive with the current solar system constraints for BD and SMG theories.

Relativistic Models for Strange Stars in Massive Brans–Dicke Gravity

Relativistic Models for Strange Stars in Massive Brans–Dicke Gravity

Friedmann cosmology with decaying vacuum density in Brans\u2013Dicke theory

In this paper, we study Friedmann cosmology with time-varying vacuum energy density in the context of Brans–Dicke theory. We consider an isotropic and homogeneous flat space, filled with a matter-dominated perfect fluid and a dynamical cosmological term varLambda (t) , obeying the equation of state of the vacuum. As the exact nature of a possible time-varying vacuum is yet to be found, we explore varLambda (t) given by the phenomenological law varLambda (t)=lambda +sigma H, where lambda and sigma are positive constants. We solve the model and then focus on two different cases varLambda _{H1} and varLambda _{H2} by assuming varLambda =lambda and varLambda =sigma H, respectively. Notice that varLambda _{H1} is the analog of the standard varLambda CDM, but within the Brans–Dicke cosmology. We find the analytical solution of the main cosmological functions such as the Hubble parameter, the scale factor, deceleration and equation of state parameters for these models. In order to test the viability of the cosmological scenarios, we perform two sets of joint observational analyses of the recent Type Ia supernova data (Pantheon), observational measurements of Hubble parameter data, Baryon acoustic oscillation/Cosmic microwave background data and Local Hubble constant for each model. For the sake of comparison, the same data analysis is performed for the varLambda CDM model. Each model shows a transition from decelerated phase to accelerated phase and can be viewed as an effective quintessence behavior. Using the model selection criteria AIC and BIC to distinguish from existing dark energy models, we find that the Brans–Dicke analog of the varLambda -cosmology (i.e. our model varLambda _{H1}) performs at a level comparable to the standard varLambda CDM, whereas varLambda _{H2} is less favoured.

Constraints on holographic dark energy model with matter creation in Brans–Dicke theory and thermodynamic analysis

The adiabatic matter creation for a spatially flat, homogeneous and isotropic universe is discussed in holographic dark energy (HDE) in the context of Brans–Dicke theory. Since the HDE density is considered as a dynamical cosmological constant, it is natural to study it in a dynamical frame of Brans–Dicke theory. We show that HDE model with matter creation, whose infrared cutoff is set by the Hubble horizon, leads to solution that unify the early and late time acceleration. The latest observational data from supernovae (Pantheon sample), Hubble H ( z ) and latest local H 0 by SH0ES are used for constraining the model parameters. Using the Markov chain Monte Carlo method, we obtain the best fit values of the parameters for different models. It is found that the HDE model without matter creation does not achieve transition phase when the Hubble horizon is taken as an IR cut-off. However, it achieves the phase transition from decelerated phase to accelerated phase with same IR cut-off with the inclusion of gravitationally induced matter creation. The best fit values of HDE model with matter creation are fitted very well in Hubble error data. Using AIC and BIC, and geometrical diagnostic parameters, we compare the models with Λ CDM model and discuss the viability of the model. A detailed thermodynamic analysis is also carried out.

Difficulties in reconciling non-negligible differences between the local and cosmological values of the gravitational coupling in extended Brans-Dicke theories

Recent studies by Solà Peracaula, Gómez-Valent, de Cruz Pérez and Moreno-Pulido (2019,2020) have pointed out the intriguing possibility that Brans-Dicke cosmology with constant vacuum energy density (BD-ΛCDM) may be able to alleviate the H 0 and σ 8 tensions that are found in the framework of the concordance cosmological model (GR-ΛCDM). The fitting analyses presented in these works indicate a preference for values of the effective gravitational coupling appearing in the Friedmann equation, G, about 4–9% larger than Newton's constant (as measured on Earth), and mildly evolving with the expansion of the universe. The signal reaches the ∼ 3.5σ c.l. when the prior on H 0 from SH0ES and the angular diameter distances to strong gravitationally lensed quasars measured by H0LICOW are considered, and the ∼ 3σ c.l. when only the former is included. Thus, the improvement in the description of the cosmological datasets relies on the existence of a mechanism capable of screening the modified gravity effects at those scales where deviations from standard General Relativity (GR) are highly constrained, as in the Solar System. In this paper we explore several extensions of BD-ΛCDM that can leave the cosmological evolution basically unaltered at the background and linear perturbations level, while being able to screen the Brans-Dicke effects inside the regions of interest, leading to standard GR. We search for weak-field solutions around spherical static massive objects with no internal pressure and show that, unfortunately, these mechanisms can only explain very tiny departures of the effective cosmological gravitational coupling from the one measured locally. This might hinder the ability of BD-ΛCDM to alleviate the cosmological tensions.

Determination of time evolution of the gravitational constant in the framework of Brans-Dicke Theory: An easy wa

The present article demonstrates a very simple mathematical way to determine the time-dependence of the dynamical gravitational constant () in the framework of the Brans-Dicke theory of gravity. Brans-Dicke field equations, for a matter-dominated, pressure-less and spatially flat universe with homogeneous and isotropic space-time, have been used for this formulation. The gravitational constant () is the reciprocal of the Brans-Dicke scalar field (). Using a simple ansatz, which represents the Brans-Dicke scalar field () as a function of time, the possible values of a constant parameter (constituting the ansatz) have been calculated with the help of the field equations, using the values of some cosmological parameters at the present time. The values of that parameter (belonging to the ansatz) lead to the conclusion that the scalar field () decreases and consequently the gravitational constant () increases with time. The value of the relative time-rate of change of the gravitational constant (i.e., ) has also been estimated and this quantity has been found to be independent of time. Time-dependence of and has been depicted graphically for all values of the parameter belonging to the ansatz. The novel features of this study are that the gravitational field equations did not have to be solved, unlike other studies, to arrive at the results and the mathematical scheme for calculations is extremely easy in comparison to other recent studies in this regard.

Post-Newtonian γ -like parameters and the gravitational slip in scalar-tensor and f(R) theories

We review the fundamentals and highlight the differences between some commonly used definitions for the PPN gamma parameter ($\ensuremath{\gamma}$) and the gravitational slip ($\ensuremath{\eta}$). Here we stress the usefulness of a gammalike parameter used by Berry and Gair (${\ensuremath{\gamma}}_{\mathrm{\ensuremath{\Sigma}}}$) that parametrizes the bending of light and the Shapiro time delay in situations in which the standard $\ensuremath{\gamma}$ cannot be promptly used. First we apply our considerations to two well-known cases, but for which some conflicting results can be found: massive Brans-Dicke gravity and $f(R)$ gravity (both the metric and the Palatini versions). Although the slip parameter is always well defined, it has in general no direct relation to either light deflection or the Shapiro time delay, hence care should be taken on imposing the PPN $\ensuremath{\gamma}$ bounds on the slip. We stress that, for any system with a well-posed Newtonian limit, Palatini $f(R)$ theories always have $\ensuremath{\gamma}=1$; while metric $f(R)$ theories can only have two values: either 1 or $1/2$. The extension toward Horndeski gravity shows no qualitative surprises, and ${\ensuremath{\gamma}}_{\mathrm{\ensuremath{\Sigma}}}$ is a constant in this context (only assuming that the Horndeski potentials can be approximated by analytical functions). This implies that a precise study on the bending of light for different impact parameters can in principle be used to rule out the complete Horndeski action as an action for gravity. Also, we comment on the consequences for $\ensuremath{\gamma}$ inferences at external galaxies.

Quantum and Classical Cosmology in the Brans–Dicke Theory

In this paper, we discuss classical and quantum aspects of cosmological models in the Brans–Dicke theory. First, we review cosmological bounce solutions in the Brans–Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then, we quantize this classical model in a canonical way, establishing the corresponding Wheeler–DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case ω<−32, the energy is bounded from below and singularity-free solutions are found. However, in the case ω>−32, we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite (energy spectrum is not bounded from below). However, we can analyze this case using Bohmian mechanics and the de Broglie–Bohm interpretation of quantum mechanics. Using this approach, the classical and quantum results can be compared for any value of ω.

Anisotropic stars via embedding approach in Brans\u2013Dicke gravity

In the present article, the solution of the Einstein–Maxwell field equations in the presence of a massive scalar field under the Brans-Dicke (BD) gravity is obtained via embedding approach, which describes a charged anisotropic strange star model. The interior spacetime is described by a spherically symmetric static metric of embedding class I. This reduces the problem to a single-generating function of the metric potential which is chosen by appealing to physics based on regularity at each interior point of the stellar interior. The resulting model is subjected to rigorous physical checks based on stability, causality and regularity for particular object PSR J1903+327. We also show that our solutions describe compact objects such as PSR J1903+327; Cen X-3; EXO 1785-248 and LMC X-4 to an excellent approximation. Novel results of our investigation reveal that the scalar field leads to higher surface charge densities which in turn affects the compactness and upper and lower values imposed by the modified Buchdahl limit for charged stars. Our results also show that the electric field and scalar field which originate from entirely different sources couple to alter physical characteristics such as mass-radius relation and surface redshift of compact objects. This superposition of the electric and scalar fields is enhanced by an increase in the BD coupling constant, omega _{BD}.

Komar integrals for theories of higher order in the Riemann curvature and black-hole chemistry

We construct Komar-type integrals for theories of gravity of higher order in the Riemann curvature coupled to simple kinds of matter (scalar and vector fields) and we use them to compute Smarr formulae for black-hole solutions in those theories. The equivalence between f (R) and Brans-Dicke theories is used to argue that the dimensionful parameters that appear in scalar potentials must be interpreted as thermodynamical variables (pressures) and we give a general expression for their conjugate potentials (volumes).

Phase space correspondence between Jordan and Einstein frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

Observational data analysis for generalized cosmic Chaplygin gas in the background of Brans–Dicke theory

In this paper, we have considered the generalized cosmic Chaplygin gas (GCCG) in the background of Brans–Dicke (BD) theory and also assumed that the Universe is filled in GCCG, dark matter and radiation. To investigate the data fitting of model parameters, we have constrained the model using recent observations. Using [Formula: see text] minimum test, the best-fit values of the model parameters are determined by OHD+CMB+BAO+SNIa joint data analysis. We have drawn the contour figures for different confidence levels [Formula: see text], [Formula: see text] and [Formula: see text]. To examine the viability of the GCCG model in BD theory, we have also determined △AIC and △BIC using the information criteria (AIC and BIC). Graphically, we have analyzed the natures of the equation of state parameter and deceleration parameter for our best-fit values of model parameters. Also, we have studied the square speed of sound [Formula: see text] which lies in the interval [Formula: see text] for expansion of the Universe. So, our considered model is classically stable by considering the best-fit values of the model parameters due to the data analysis.