Weak field gravitational wave solutions are investigated in Brans–Dicke (BD) theory in the presence of a cosmological constant. In this setting the background geometry is not flat but asymptotically de-Sitter. We investigate the linearised field equations, and their gravitational wave solutions in a certain gauge choice. We will show that this theory leads to massless scalar waves as in original BD theory and in contrast to massive BD theory. The effects of these waves on free particles and their polarization properties are studied extensively and effects of the cosmological constant is analyzed in these phenomena in detail. The energy flux of these waves are also discussed in this background. By analyzing this flux, we obtain a critical distance where the waves cannot propagate further, which extends Cosmic no Hair Conjecture (CNC) to BD theory with a cosmological constant.

A mysterious dark matter is supposed to exist in the galactic halos. In this contrast, we discuss the possibility of explaining the flat rotational velocity curves in f(R) gravity by solving field equations numerically in vacuum and for different matter distributions. For a spherically symmetric static space-time (as the galactic environment) we give metric for constant rotational velocity regions. For a constant rotational velocity region, we prove that all values of rotational velocities (most importantly observed rotational velocity 200–300 Km/s) do not lead to an analytic solution of the vacuum field equations. We then obtain numerical solutions of the field equations in vacuum and for three types of mass distributions named: (1) power law density profile, (2) simple model for galaxy with a core and, (3) Navarro, Frank and White (NFW) profile, for M31 and Milky way galaxy. The solutions suggest a slight modification from linear relations from R for vacuum whereas a significant deviation from R for the distributions can give flat rotational curves. Using Brans-Dicke theory, we also relate obtained modified gravity function with the equivalent scalar fields, the procedure gives us very interesting phenomena and behavior of dark matter in the galactic environment. We observe that the scalar dark matter, coming from different modified gravity functions of matter profiles, does not accumulate as the baryonic matter. These results then can be used to explain the spatial offset of the center of the total mass from the center of the baryonic mass peaks of the bullet cluster and Abell-520.

Effects of charge on decoupled solutions in self-interacting Brans–Dicke theory

In this paper, we explore the behavior and anisotropic structure of quark stellar models in the framework of massive Brans–Dicke gravity. The system of field equations, representing a static sphere, is formulated by incorporating the MIT bag model. We use the Karmarkar condition for embedding class-one to formulate a relativistic model corresponding to a well-behaved radial metric function. The values of unknown parameters are determined through the matching of internal and external space–times at the hypersurface. The observed masses and radii of the strange star candidates (RXJ 1856-37, Her X-1 and PSR J1614-2230) specify the solution. Further, we evaluate the impact of the massive scalar field on state parameters and investigate the viability as well as stability of the self-gravitating objects. It is found that the obtained values of the bag constant (corresponding to each star) lie within the accepted range. Moreover, the anisotropic structure meets the necessary viability and stability criteria.

Geodesic deviation equation in Brans–Dicke theory in arbitrary dimensions

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.

In this paper, we compute an anisotropic cosmological solution through a minimal geometric deformation on a non-static spherical spacetime in the framework of self-interacting Brans-Dicke theory. The transformation of the radial component decouples the field equations into two arrays such that the influence of the anisotropic source is limited to one set only. We use FLRW universe model to obtain a solution of the system governed by the isotropic matter source. For this purpose, power-law models of the scale factor as well as massive scalar field are assumed while isotropic pressure and density are related via barotropic equation of state. The decoupling function, appearing in the other set, is evaluated through the conservation equation of the anisotropic source. Finally, we investigate the physical behavior, viability and stability of the extended FLRW solution for different values of the equation of state parameter. It is concluded that the solution is viable and stable for the massless scalar field and the radiation dominated universe.

We propose a Lagrangian formulation for a varying G Newtonian-like theory inspired by the Brans–Dicke gravity. Rather than imposing an ad hoc dependence for the gravitational coupling, as previously done in the literature, in our proposal, the running of G emerges naturally from the internal dynamical structure of the theory. We explore the features of the resulting gravitational field for static and spherically symmetric mass distributions as well as within the cosmological framework.

In this cosmological model, we have studied the spatially homogeneous and anisotropic Bianchi type and axially symmetric model filled with dark matter and dark energy in Brans-Dicke’s [1] theory of gravitation. Here, we consider the modified holographic Ricci dark energy defined by Chen and Jing [21] as the suitable condition of dark energy. To obtain a solution we assumed the scale factor used Mishra et al. [43]. We have solved field equations of Brans-Dicke theory of gravitation with the help of an axially symmetric anisotropic Bianchi-type space-time. We have determined the cosmological parameters, namely, EoS parameter, MHRDE density, matter density, skewness parameter, and BD scalar field. Here the various phenomena like the expanding universe, and shift from anisotropy to isotropy are observed in this model. A detailed physical discussion of these dynamical parameters are presented graphically. Some physical and geometrical behaviours of the models are also discussed and found to be in good agreement with the recent observations (OHD+JLA) datasets.

The asymptotic symmetries in the Brans-Dicke theory are analyzed using Penrose's conformal completion method, which is independent of the coordinate system used. These symmetries, indeed, include supertranslations and Lorentz transformations for an asymptotically flat spacetime. With the Wald-Zoupas formalism, “conserved charges” and fluxes of the Bondi-Metzner-Sachs algebra are computed. The scalar degree of freedom contributes only to the Lorentz boost charge, even though it plays a role in various fluxes. The flux-balance laws are further applied to constrain the displacement memory, spin memory, and center-of-mass memory effects.

Jordan and Einstein frame are studied under the light of Hamiltonian formalism. Dirac's constraint theory for Hamiltonian systems is applied to Brans-Dicke theory in the Jordan Frame. In both Jordan and Einstein frame, Brans-Dicke theory has four secondary first class constraints and their constraint algebra is closed. We show, contrary to what is generally believed, the Weyl (conformal) transformation, between the two frames, is not a canonical transformation, in the sense of Hamiltonian formalism. This addresses quantum mechanical inequivalence as well. A canonical transformation is shown.

In this paper, we formulate black hole solutions through extended gravitational decoupling scheme in the framework of self-interacting Brans-Dicke theory. The addition of a new source in the matter distribution increases the degrees of freedom in the system of field equations. Transformations in radial as well as temporal metric functions split the system into two arrays. Each array includes the effects of only one source (either seed or additional). The seed source is assumed to be a vacuum and the corresponding system is specified through the Schwarzschild metric. In order to construct a suitable solution of the second system, constraints are applied on the metric potentials and energy-momentum tensor of the additional source. We obtain three solutions corresponding to different values of the decoupling parameter in the presence of a massive scalar field. The extra source is classified as normal or exotic through energy conditions. It is found that two solutions agree with the energy bounds and thus have normal matter as their source.

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 the parameters of modified Chaplygin gas in Brans–Dicke theory

In this paper, we investigate a scalar field Brans–Dicke cosmological model in Lyra’s geometry which is based on the modifications in a geometrical term as well as energy term of Einstein’s field equations. We have examined the validity of the proposed cosmological model on the observational scale by performing statistical analysis from the latest [Formula: see text] and SN Ia observational data. We find that the estimated values of Hubble’s constant and matter energy density parameter is in agreement with their corresponding values, obtained from recent observations of Wilkinson Microwave Anisotropy Probe (WMAP) and Plank collaboration. We also derived the deceleration parameter, age of the universe and jerk parameter in terms of red-shift and computed its present values. The dynamics of the deceleration parameter in the derived model of the universe show a signature flipping from positive to a negative value and also indicate that the present universe is in the accelerating phase.

We study the gravitational waves emitted by an inspiraling compact binary system in massive Brans-Dicke theory. In addition to the two tensor polarizations, which have been obtained in previous work, we explicitly and analytically calculate the expressions for the time-domain waveforms of the two scalar polarizations. With the stationary phase approximations, we obtain the Fourier transforms of the two tensor polarizations. We find that when the scalar field is light, the waveforms can be mapped to the parametrized post-Einsteinian (ppE) framework, and we identify the ppE parameters. However, when the scalar field is heavy, the ppE framework is not applicable. We also obtain the projected constraints on the parameters of this theory by gravitational wave observations of future ground-based detectors. Finally, we apply our result to the model proposed by Damour and Esposito-Far\`ese, $f(R)$ gravity, and screened modified gravity.

We compare Mercury’s precession test in standard general relativity, Brans–Dicke theories (BD), and Palatini f({mathcal {R}})-theories. We avoid post-Newtonian approximation and compute exact precession in these theories. We show that the well-known mathematical equivalence between Palatini f({mathcal {R}})-theories and a specific subset of BD theories does not extend to a really physical equivalence among theories since equivalent models still allow a different incompatible precession for Mercury depending on the solution one chooses. As a result one cannot use BD equivalence to rule out Palatini f({mathcal {R}})-theories. On the contrary, we directly discuss that Palatini f({mathcal {R}})-theories can (and specific models do) easily pass Solar System tests as Mercury’s precession.

A generalized Brans-Dicke (GBD) theory in the framework of Palatini formalism is proposed in this paper. We derive the field equations by using the variational approach and obtain the linearized equations by using the weak-field approximation method. We show various properties of the geometrical scalar field in the Palatini-formalism of GBD theory: it is massless and source-free, which are different from the results given in the metric-formalism of GBD theory. Also, we investigate the polarization modes of gravitational waves (GWs) by using the geodesic deviation method and the Newman-Penrose method in the Palatini-GBD theory. It is observed that there are three polarizations modes and four oscillations in the Palatini-GBD theory. Concretely, they are the two transverse tensor (+) and (×) standard polarization modes, and one breathing mode (with two oscillations). The results of GWs polarization in the Palatini-GBD theory are different from that in the metric-GBD theory, where there are four polarizations modes: the two standard tensorial modes (+ and ×), a scalar breathing mode, and a massive scalar mode that is a mix of the longitudinal and the breathing polarization. Comparing with the Palatini-f(R˜) theory and the General Relativity, we can see that the extra breathing mode of GWs polarization can be found in the Palatini-GBD theory. At last, the expression of the parameterized post Newton (PPN) parameter is derived, which could pass through the experimental test.

Transitioning universe with hybrid scalar field in Bianchi I space–time

In the present study, we comment on Brans-Dicke scalar field cosmological model in Lyra's geometry [Maurya \& Zia, Phys. Rev. D \textbf{100}, 023503 (2019)]. In this comment, we investigate that there is no acceleration in the model proposed by the authors of Phys. Rev. D \textbf{100}, 023503 (2019). Therefore, despite the claims to the contrary the Brans-Dicke Scalar Field Cosmological Model in Lyra's Geometry with high Brans-Dicke (BD) coupling parameter $\omega$ and constant $\beta$ can not produce late time acceleration in the universe.