Brans-Dicke Theory Of Gravity Research Articles

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.

Interacting Rényi Holographic Dark Energy in the Brans-Dicke Theory

In this work, we construct an interacting model of the Rényi holographic dark energy in the Brans-Dicke theory of gravity using Rényi entropy in a spatially flat Friedmann-Lemaître-Robertson-Walker Universe considering the infrared cut-off as the Hubble horizon. In this setup, we then study the evolutionary history of some important cosmological parameters, in particular, deceleration parameter, Hubble parameter, equation of state parameter, and Rényi holographic dark energy density parameter in both nonflat Universe and flat Universe scenarios and also observe satisfactory behaviors of these parameters in the model. We find that during the evolution, the present model can give rise to a late-time accelerated expansion phase for the Universe preceded by a decelerated expansion phase for both flat and nonflat cases. Moreover, we obtain ω D → − 1 as z → − 1 , which indicates that this model behaves like the cosmological constant at the future. The stability analysis for the distinct estimations of the Rényi parameter δ and coupling coefficient b 2 has been analyzed. The results indicate that the model is stable at the late time.

Evolution of FLRW universe in Brans-Dicke gravity theory

This study aims to examine the dynamics of flat Friedmann-Lemaitre-Robertson-Walker (FLRW) model of universe with time varying cosmological constant $\Lambda (t)$ in Brans-Dicke theory of gravity. The authors find a solution of the field equations using simple parametrization of scale factor $a(t)$ i.e. $a(t)=\exp \{(\alpha t+\beta )^{p}\}$ , and power law relation between $a(t)$ and Brans-Dicke scalar field $\phi $ . The derived cosmological model shows transition from early cosmic deceleration to present cosmic acceleration. Such feature of cosmic expansion is in agreement with recent empirical observations. The behaviour of cosmographic parameters such as Hubble parameter, deceleration parameter, jerk, snap and lerk parameters is examined graphically. It is observed that model behaves like $\Lambda CDM$ model in late cosmic evolution. We also use statefinder and Om diagnostic tools to differentiate various dark energy models from $\Lambda CDM$ model. Moreover, model parameter $p$ and present value of deceleration parameter $q_{0}$ is also estimated using Hubble data set and Pantheon Type 1a supernova data set.

Constraining an exact Brans–Dicke gravity theory with recent observations

In this paper first we study Brans-Dicke equations with the cosmological constant to find an exact solution in the spatially flat Robertson-Walker metric. Then we use Observational Hubble data, the baryon acoustic oscillation distance ratio data as well as cosmic microwave background data from Planck to constrain parameters of the obtained Brans-Dicke model. To compare our results and find out the amount of deviation from general relativity, we also constrain concordance cosmological model using the same data. In our theoretical model the Brans-Dicke coupling constant is replaced by a , say new, parameter namely \textgravedbl scalar field density $\Omega_{\phi}$\textacutedbl. Therefore, as $\Omega_{\phi}\to 0$ which is equivalent to $\omega\to \infty$ general relativity is recovered. In general, we found no significant deviation from general relativity. Our estimations show $\Omega_{\phi}=0.010^{+0.021}_{-0.012}$ which is equivalent to $\omega>1560$ at $95\%$ confidence level. We also obtained constraint the rate of change of gravitational constant, $\dot{G}/G$, at present time as $1.150\times 10^{-13}yr^{-1}<\dot{G}/G<1.198\times 10^{-13}yr^{-1}$ (at $1\sigma$ error). The total variation of gravitational constant, since the epoch of recombination, is also constrained as $-0.0084<\delta G/G<-0.0082$ at $68\%$ confidence level.

Five-dimensional Brans–Dicke compactified universe dominated by a varying speed of light

We extend the model of a 5D Brans–Dicke gravity theory reduced to 4D through the presence of a hypersurface-orthogonal space-like killing vector field in the underlying 5D spacetime by including a varying speed of light. The resulting model is characterized by the presence of two scalar fields. We focus on late-time power law solutions which emerge in general when scalar fields couple to spacetime curvature and do not contradict the SNIa astrophysical data. Analytic solutions in 4-dimensions are derived and late-time accelerated expansion was found. The universe is dominated by dark energy, free from phantom field and is characterized by a decaying energy matter density, decaying scalar fields, and a decreasing celerity of light. The model is confronted with astrophysical observations and is found to fit these data.

Testing Brans-Dicke gravity with screening by scalar gravitational wave memory

The Brans-Dicke theory of gravity is one of the oldest ideas to extend general relativity by introducing a nonminimal coupling between the scalar field and gravity. The Solar System tests put tight constraints on the theory. In order to evade these constraints, various screening mechanisms have been proposed. These screening mechanisms allow the scalar field to couple to matter as strongly as gravity in low density environments while suppressing it in the Solar System. The Vainshtein mechanism, which is found in various modified gravity models such as massive gravity, braneworld models and scalar tensor theories, suppresses the scalar field efficiently in the vicinity of a massive object. This makes it difficult to test these theories from gravitational wave observations. We point out that the recently found scalar gravitational wave memory effect, which is caused by a permanent change in spacetime geometry due to the collapse of a star to a back hole can be significantly enhanced in the Brans-Dicke theory of gravity with the Vainshtein mechanism. This provides a possibility to detect scalar gravitational waves by a network of three or more gravitational wave detectors.

Scalar stochastic gravitational-wave background in Brans-Dicke theory of gravity

We study the scalar stochastic gravitational-wave background (SGWB) from astrophysical sources, including compact binary mergers and stellar collapses, in the Brans-Dicke theory of gravity. By contrast to tensor waves, the scalar SGWB predominantly arises from stellar collapses. These collapses not only take place at higher astrophysical rates but also emit more energy. This is because, unlike tensor radiation which mainly starts from quadrupole order, the scalar perturbation can be excited by changes in the monopole moment. In particular, in the case of stellar collapse into a neutron star or a black hole, the monopole radiation, at frequencies below 100 Hz, is dominated by the memory effect. At low frequencies, the scalar SGWB spectrum follows a power law of ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{S}}\ensuremath{\propto}{f}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}=1$. We predict that ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{S}}$ is inversely proportional to the square of ${\ensuremath{\omega}}_{\mathrm{BD}}+2$, with $({\ensuremath{\omega}}_{\mathrm{BD}}+2{)}^{2}{\mathrm{\ensuremath{\Omega}}}_{S}(f=25\text{ }\text{ }\mathrm{Hz})=2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. We also estimate the detectability of the scalar SGWB for current and third-generation detector networks and the bound on ${\ensuremath{\omega}}_{\mathrm{BD}}$ that can be imposed from these observations.

Vaidya spacetime in Brans\u2013Dicke gravity\u2019s rainbow

In this note we study an energy dependent deformation of a time dependent geometry in the background of Brans–Dicke gravity theory. The study is performed using the gravity’s rainbow formalism. We compute the field equations in Brans–Dicke gravity’s rainbow using Vaidya metric which is a time dependent geometry. We study a star collapsing under such conditions. Our prime objective is to determine the nature of singularity formed as a result of gravitational collapse and its strength. The idea is to test the validity of the cosmic censorship hypothesis for our model. We have also studied the effect of such a deformation on the thermalization process. In this regard we have calculated the important thermodynamical quantities such as thermalization temperature, Helmholtz free energy, specific heat and analyzed the behavior of such quantities.

Thermodynamics of 4-dimensional charged black holes in Brans-Dicke-Born-Infeld gravity theory

In this work, the charged black hole solution to the Brans-Dicke gravity theory in the presence of the nonlinear electrodynamics has been investigated. To simplify the field equations, a suitable conformal transformation has been used which transforms the Brans-Dicke-Born-Infeld Lagrangian to that of Einstein-dilaton theory with new nonlinear electrodynamics field. A new class of 4-dimensional black hole solution has been constructed out as the exact solution to the Brans-Dicke theory in the presence of the Born-Infeld nonlinear electrodynamics. The physical properties of the solutions have been studied. The black hole charge and temperature have been calculated making use of the Gauss’s law and the concept of surface gravity, respectively. Also, the black hole mass and entropy have been obtained from geometrical methods. Through a Smarr-type mass formula as a function of the black hole charge and entropy the black hole temperature and electric potential, as the intensive parameters conjugate to the black hole entropy and charge, have been calculated.

Thermodynamics of nonlinearly charged black holes in the Brans\u2013Dicke modified gravity theory

In this work, the charged black hole solution to the Brans–Dicke gravity theory in the presence of the nonlinear electrodynamics has been investigated. To simplify the field equations, a conformal transformation has been introduced which transforms the Brans–Dicke–Born–Infeld Lagrangian to that of Einstein-dilaton–Born–Infeld theory. A new class of (n+1)-dimensional black hole solution has been constructed out as the exact solution to the Brans–Dicke theory in the presence of the Born–Infeld nonlinear electrodynamics. The physical properties of the solutions have been studied. The black hole charge and temperature have been calculated making use of the Gauss’s law and the concept of surface gravity, respectively. Also, the black hole mass and entropy have been obtained from geometrical methods. Trough a Smarr-type mass formula as a function of the black hole charge and entropy the black hole temperature and electric potential, as the intensive parameters conjugate to the black hole entropy and charge, have been calculated. The consistency of results of the geometrical and thermodynamical approaches confirms the validity of the first law of black hole thermodynamics for this new black hole solution. Finally, making use of the ensemble canonical method, the local stability or phase transition of the new (n+1)-dimensional Brans–Dicke–Born–Infeld black hole solution has been analyzed.

A Bianchi type-II dark-energy cosmology with a decaying Λ-term in the Brans–Dicke theory of gravity

This paper deals with a spatially homogeneous and totally anisotropic Bianchi type-V cosmological model within the framework of self interacting Brans Dicke theory of gravity in the background of anisotropic dark energy (DE) with variable equation of state (EoS) parameter and constant deceleration parameter. Constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. EoS parameter {\omega} and its existing range for the models is in good agreement with the most recent observational data. We notice that {\omega} given by (37) i.e {\omega}(t) = log(k1t) is more suitable in explaining the evolution of the universe. The physical behaviors of the solutions have also been discussed using some physical quantities. Finally, we observe that despite having several prominent features, both of the DE models discussed fail in details.

The maximum sizes of large scale structures in alternative theories of gravity

The maximum size of a cosmic structure is given by the maximum turnaround radius—the scale where the attraction due to its mass is balanced by the repulsion due to dark energy. We derive generic formulae for the estimation of the maximum turnaround radius in any theory of gravity obeying the Einstein equivalence principle, in two situations: on a spherically symmetric spacetime and on a perturbed Friedman-Robertson-Walker spacetime. We show that the two formulae agree. As an application of our formula, we calculate the maximum turnaround radius in the case of the Brans-Dicke theory of gravity. We find that for this theory, such maximum sizes always lie above the ΛCDM value, by a factor 1 + 1/3ω, where ω≫ 1 is the Brans-Dicke parameter, implying consistency of the theory with current data.

Instability analysis of a cylindrical stellar object in Brans–Dicke gravity

This paper investigates instability ranges of a cylindrically symmetric collapsing stellar object in Brans-Dicke theory of gravity. For this purpose, we use perturbation approach in the modified field equations as well as dynamical equations and construct a collapse equation. The collapse equation with adiabatic index ($\Gamma$) is used to explore the instability ranges of both isotropic as well as anisotropic fluid in Newtonian and post-Newtonian approximations. It turns out that the instability ranges depend on the dynamical variables of collapsing fluid. We conclude that the system always remains unstable for $0<\Gamma<1$ while $\Gamma>1$ provides instability only for the special case.

FRW cosmological models in Brans-Dicke theory of gravity with variable q $q$ and dynamical Λ $\varLambda$ -term

Exact solution of modified Einstein’s field equations are considered within the scope of spatially homogeneous and isotropic Fraidmann-Robertson-Walker (FRW) space-time filled with perfect fluid in the frame work of Brans-Dicke scalar-tensor theory of gravity. In this paper we have investigated the flat, open and closed FRW models and the effect of dynamic cosmological term on the evolution of the universe. Two types of FRW cosmological models are obtained by setting the power law between the scalar field $\phi$ and the scale factor $a$ and deceleration parameter (DP) $q$ as a time dependent. The concept of time dependent DP with some proper assumptions yield two type of the average scale factors (i) $a(t)=[\sinh(\alpha t)]^{\frac{1}{n}}$ and (ii) $a(t)=[t^{\alpha}e^{t}]^{\frac{1}{n}}$ , $\alpha$ and $n\neq 0$ are arbitrary constants. In case (i), for $0 < n \leq 1$ , it generates a class of accelerating models while for $n > 1$ , the models of the universe exhibit phase transition from early decelerating to present accelerating phase and the transition redshift $z_{t}$ has been calculated and found to be in good agreement with the results from recent astrophysical observations. In case (ii), for $n \geq 2$ and $\alpha = 1$ , we obtain a class of transit models of the universe from early decelerating to present accelerating phase. Taking into consideration the observational data, we conclude that the cosmological constant behaves as a positive decreasing function of time. The physical and geometric properties of the models are also discussed with the help of graphical presentations.

Remarks about the correspondence between f(R) and Brans–Dicke gravity theories

We discuss the correspondence between metric [Formula: see text] gravity and [Formula: see text] Brans–Dicke theory with a potential, by working out an example that reconfirms this equivalence.

Metric factorizability and equivalence of brane world models with Brans-Dicke theory

In the standard brane world models, the bulk metric ansatz is usually assumed to be factorizable in brane and bulk coordinates. However, it is not self-evident that it is always possible to factorize the bulk metric. Using the gradient expansion scheme, which involves the expansion of bulk quantities in terms of the brane-to-bulk curvature ratio as a perturbative parameter, we explicitly show that metric factorizability is a valid assumption up to second order in the perturbative expansion. We also argue from our result that the same should be true for all orders in the perturbation scheme. We further establish that the nonlocal terms present in the bulk gravitational field equation can be replaced by the radion field; the effective action on the brane thereby obtained resembles the Brans-Dicke theory of gravity.

Time-varying gravitomagnetism in Brans-Dicke theory of gravity

Time-varying gravitomagnetism in Brans-Dicke theory of gravity

Refractive index associated with global monopole spacetime in the Brans-Dicke theory of gravity

Refractive index associated with global monopole spacetime in the Brans-Dicke theory of gravity

Radiation drag in Brans-Dicke theory of gravity

The orbital motion of a test particle near a non-rotating star with a high and uniform luminosity is explored in the context of the Brans-Dicke gravity. Just as in the Einstein gravity, from the equation of motion for the test particle, we found that a “suspension surface” exists, where the test particle comes to rest. Unlike in the Einstein gravity, the radial position of the suspension surface depends on the BD parameter ω as well as the luminosity of the star, but is independent of the initial position and velocity of the particle. As the BD parameter ω gets larger, the position of the “suspension surface” in the BD gravity approaches that in the Einstein gravity as it should. However, when the value of the parameter ω is small, i.e., ω ~ 1, the suspension’s position in the BD gravity deviates significantly from that in the Einstein gravity. Among others, however, the most remarkable lesson we learned in the present study is that the true and detailed nature of an alternative theory of gravity is not available in the complete absence of a test particle with motion.

Newtonian limit and general radial coordinate in the Brans-Dicke theory of gravity

Newtonian limit and general radial coordinate in the Brans-Dicke theory of gravity