Recently, there has been much interest in investigating outstanding problems of cosmology with modified theories of gravity. The Brans-Dicke theory of gravity is one such theory developed by Brans and Dicke absorbing Mach’s principle into the General Theory of Relativity. In Brans-Dicke theory, gravity couples with a time-dependent scalar field ϕ through a coupling parameter ω. This theory reduces to the General Theory of Relativity if the scalar field ϕ is constant and the coupling parameter ω →∞. In this paper, we consider a flat Friedmann-Lemaıtre-Robertson-Walker (FLRW) universe with a time-dependent cosmological constant in Brans-Dicke theory of gravity. Exact solutions of the field equations are obtained by using a power law relation between the scale factor and the Brans-Dicke scalar field ϕ and by taking the Hubble parameter H to be a hyperbolic function of the cosmic time t. We study the cosmological dynamics of our model by graphically representing some important cosmological parameters such as the deceleration parameter, energy density parameter, equation of state parameter, jerk parameter, snap parameter, lerk parameter etc. The statefinder diagnostic pair of the model is also obtained and the validity of the four energy conditions, viz. the Strong energy condition (SEC), Weak energy condition (WEC), Dominant energy condition (DEC) and Null energy condition (NEC), is examined. We find that the universe corresponding to our model is expanding throughout its evolution and exhibits late time cosmic acceleration, which is in agreement with the current observational data.

In the present paper, we study Barrow holographic dark energy in Brans-Dicke theory of gravity for flat Frieddman-Lemaitre-Robertson-Walker metric. We have assumed power law form of Brans-Dicke scalar field in terms of scale factor . The thermodynamics analysis of the model is discussed. It is observed that the model satify generalized second law of thermodynamics for all values of the parameter in past, present as well as in the future universe.

This paper investigates and examines a wide range of findings related to the description of holographic Ricci dark energy (HRDE) with the bulk viscosity within Universe's late-time accelerated expansion in the framework of an anisotropic Bianchi type-III cosmological model with pressure-less matter content in the Brans-Dicke theory of gravity. We are using the relationship between the metric potentials to obtain a precise conclusion to the field equations, resulting in a rapid expansion. Several major cosmological parameters, including Hubble, deceleration, matter energy density, Ricci dark energy density (RDE), and Equation of state (EoS), are used to investigate the physical behavior of our dark energy model. We detected some of the viscosity of the holographic Ricci dark energy model using current cosmological observations. We describe how the model's physical and geometric properties are compatible with recent compilations.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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 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.

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

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.

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.

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.