Brans-Dicke Research Articles

The Variation of G and Λ in Cosmology

The idea of varying constants of nature is very old, and has commanded a lot of attention since first mooted. The variation in the gravitational parameter G and cosmological parameter Λ is still an active area of research. Since the idea of a varying G was introduced by Dirac almost a century ago, there are even theories that have variable G such as the Brans–Dicke theory and the scale covariant theory. Both these theories also have a varying Λ in their full generalisations. A varying Λ was also introduced around the same time as that of varying G. It is interesting to note that a possible solution to the cosmological constant problem can be realised from a dynamic Λ. In this work, we focus on a varying Λ and G framework. In almost all studies in the simplest framework of variables Λ and G, it is found that one of them has to increase with time. However, observations and theoretical considerations indicate that both Λ and G should decrease with time. In this paper, we propose a solution to this problem, finding theories in which both Λ and G decrease with time.

Cosmological singularity and power-law solutions in modified gravity

A bouncing Universe avoids the big-bang singularity. Using the time-like and null Raychaudhuri equations, we explore whether the bounce near the big-bang, within a broad spectrum of modified theories of gravity, allows for cosmologically relevant power-law solutions under reasonable physical conditions. Our study shows that certain modified theories of gravity, such as Stelle gravity, do not demonstrate singularity resolution under any reasonable conditions, while others including f(R) gravity and Brans–Dicke theory can demonstrate singularity resolution under suitable conditions. For these theories, we show that the accelerating solution is slightly favoured over ekypyrosis.

Thermodynamics analysis of non-interacting Barrow holographic dark energy in Brans-Dicke theory

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.

Inflationary model in Brans–Dicke theory

In this paper, we present a model of inflation in the original form of Brans–Dicke (BD) theory without any modification and without adding any dark energy candidate. We consider a log function of the scale factor in the BD scalar field to discuss the inflationary era of the universe. We obtain the expressions for the deceleration parameter and the equation of state parameter, and plot their graphs against the cosmic scale factor. We observe that the universe starts with decelerated expansion and experiences an early time phase transition from a decelerated phase to an accelerated phase. After a very short period, the accelerated expansion ends in a decelerated expansion, showing the inflationary era of the cosmic evolution. To analyze the model on thermodynamic ground, we consider generalized second law of thermodynamics and observe that the law is satisfied within the model. Further, we study the stability of the model using the squared sound speed method. We plot the squared sound speed against cosmic time t and discuss the effects of the parameters on the stability of the model. We observe that for suitable values of the model parameters our model is stable.

Kinetic and hydrodynamic post-Newtonian equations in the Brans–Dicke theory

Abstract A kinetic theory for the post-Newtonian Brans–Dicke theory is developed. The Boltzmann equation and the equilibrium Maxwell-Jüttner distribution function are determined from the knowledge of the components of the metric tensor and Christoffel symbols in the post-Newtonian Brans–Dicke theory. The hydrodynamic equations for the mass density, momentum density and mass-energy density are obtained from a transfer equation derived from the Boltzmann equation. The problem of self-gravitating fluid instabilities in the post-Newtonian Brans–Dicke theory is investigated.

Revisiting Weak Energy Condition and wormholes in Brans-Dicke gravity

It is known that the formation of a wormhole typically involves a violation of the Weak Energy Condition (WEC), but the reverse is not necessarily true. In the context of Brans-Dicke gravity, the generalized Campanelli-Lousto solution, which we shall unveil in this paper, demonstrates a WEC violation that coincides with the appearance of unbounded sheets of spacetime within the region where 0<r<rs. The emergence of a wormhole in the region where r>rs is thus only an indirect consequence of the WEC violation. Whereas the two regions, 0<r<rs and r>rs, in general are disconnected by physical singularities at r=rs, they are both part of the same mathematical solution, and their behavior can provide insights into the WEC, which is a mathematical property of the solution. Furthermore, we utilize the generalized Campanelli-Lousto solution to construct a Kruskal-Szekeres diagram, which exhibits a “gulf” sandwiched between the four quadrants in the diagram, a novel feature in Brans-Dicke gravity. Overall, our findings shed new light onto a complex interplay between the WEC and wormholes in the Brans-Dicke theory.

Study on Anisotropic Dark Energy Cosmological Models in Generalized Brans-Dicke Theory

In this present paper, we have investigated the dark energy cosmological model in Bianchi−V I0 spacetime by considering generalised Brans-Dicke theory, self-interacting potential, and a dynamical coupling parameter. For this purpose, we have utilised a hybrid scale factor to approximate the dynamical behaviour of the deceleration parameter. The deceleration parameter should display distinctive flipping behaviour at the transition redshift since the universe is thought to have changed from an early deceleration to a late temporal acceleration. We have studied six alternative transitioning dark energy models on the basis of observational restrictions on the transition redshift. For each model, the behaviour of the dynamical scalarfield, the Brans-Dicke parameter, and the self-interacting potential are examined. On top of that, we used the generalised Brans-Dicke theory to estimate how the Newtonian gravitational constant changes over time.

A simple prediction of the nonlinear matter power spectrum in Brans–Dicke gravity from linear theory

Brans–Dicke (BD), one of the first proposed scalar-tensor theories of gravity, effectively makes the gravitational constant of general relativity (GR) time-dependent. Constraints on the BD parameter ω serve as a benchmark for testing GR, which is recovered in the limit ω → ∞. Current small-scale astrophysical constraints ω ≳ 105 are much tighter than large-scale cosmological constraints ω ≳ 103, but the two decouple if the true theory of gravity features screening. On the largest cosmological scales, BD approximates the most general second-order scalar–tensor (Horndeski) theory, so constraints here have wider implications. These constraints will improve with upcoming large-scale structure and cosmic microwave background surveys. To constrain BD with weak gravitational lensing, one needs its nonlinear matter power spectrum PBD. By comparing the boost B = PBD/PGR from linear theory and nonlinear N-body simulations, we show that the nonlinear boost can simply be predicted from linear theory if the BD and GR universes are parameterized in a way that makes their early cosmological evolution and quasilinear power today similar. In particular, they need the same H0/√Geff(a = 0) and σ8, where Geff is the (effective) gravitational strength. Our prediction is 1% accurate for ω ≥ 100, z ≤ 3, and k ≤ 1 h/Mpc; and 2% up to k ≤ 5 h/Mpc. It also holds for GBD that do not match Newton’s constant today, so one can study GR with different gravitational constants GGR by sending ω → ∞. We provide a code that computes B with the linear Einstein-Boltzmann solver HI_CLASS and multiplies it by the nonlinear PGR from EUCLIDEMULATOR2 to predict PBD.

Gravitational radiation in generalized Brans–Dicke theory: compact binary systems

This paper investigates the generation and properties of gravitational radiation within the framework of generalized Brans–Dicke (GBD) theory, with a specific emphasis on its manifestation in compact binary systems. The study begins by examining the weak field equations in GBD theory, laying the foundation for subsequent analyses. Solutions to the linearized field equations for point particles are then presented, providing insights into the behavior of gravitational fields in the context of GBD theory. The equation of motion of point mass is explored, shedding light on the dynamics of compact binary systems within the GBD framework. The primary focus of this study lies in the comprehensive exploration of gravitational radiation generated by compact binaries. The energy momentum tensor and the associated gravitational wave (GW) radiation power in GBD theory are investigated, elucidating the relationship between these fundamental concepts. Furthermore, detailed calculations are provided for the GW radiation power originating from both tensor fields and scalar fields. Based on our calculations, both scalar fields contribute to GW radiation by producing dipole radiation. We also study the period derivative of compact binaries in this theory. By comparing with the observational data of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR J1012+5307, we put bounds on the two parameters of the theory: the Brans–Dicke coupling parameter ω0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{0}$$\\end{document} and the mass of geometrical scalar field mf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_f$$\\end{document}, resulting in a lower bound ω0>6.09723×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{0}>6.09723\ imes 10^6$$\\end{document} for a massless BD scalar field and the geometrical field whose mass is smaller than 10-29GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-29} \ ext { GeV}$$\\end{document}. The obtained bound on ω0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _0$$\\end{document} is two orders of magnitude stricter than those derived from solar system data. Finally, we find the phase shift that GWs experience in the frequency domain during their propagation. These calculations offer a quantitative understanding of the contributions from different components within the GBD theory, facilitating a deeper comprehension of the overall behavior and characteristics of gravitational radiation.

A unimodular Kaluza-Klein theory

Unimodular gravity became an object of increasing interest in the late 80-ties (see, e.g. M. Henneaux and C. Teitelboim, (1989 Phys. Lett. B 222, 195), W. Buchmüller and N. Dragon, N. (1989 Phys. Lett. B 223, 313), W.G. Unruh, (1989 Phys. Rev. D, 40, 1048) and was recently used in primordial Universe modeling with cosmological constant, in the context of the Brans-Dicke gravity including scalar field A. M. Almeida et al (2023 Universe 8, 429). In the present article we investigate the possibility of imposing the unimodular condition within the 5-dimensional Kaluza-Klein theory including the scalar field. The variational principle is formulated in 5 dimensions first, and dimensional reduction is applied to the resulting set of equations. A cosmological model based on these equations is then presented and discussed.

Reconsidering bulk viscosity in Brans–Dicke theory

In this paper, we reconsider the concept of bulk viscosity in Brans–Dicke theory to study accelerated expansion of the universe in a flat Friedmann–Robertson–Walker metric. In recent works on bulk viscosity in Brans–Dicke theory, the power-law form of Brans–Dicke scalar field has been taken to explain recent phase transition of the universe, however, power-law form confronts constant deceleration parameter problem. Therefore, we consider recently proposed well-motivated logarithmic form of Brans–Dicke scalar field to discuss bulk viscous model in Brans–Dicke theory. We obtain the values of deceleration parameter and equation of state parameter for the model, and plot their graphs against the redshift parameter z. The plots show that the model is able to explain the recent phase transition of the universe and equation of state parameter shows the behavior of dark energy. Further, we apply two important analysis, namely, [Formula: see text] analysis and thermodynamic analysis to examine our model. The [Formula: see text] analysis shows that our model belong to thawing region and shows similarities with quintessence model. All the trajectories start from the point [Formula: see text] with different negative values of w having quintessence behavior. The thermodynamic analysis shows that the model satisfies generalized second law of thermodynamics.

Generalized Brans-Dicke cosmology, noether symmetries and quantization

A generalized Brans-Dicke theory of gravitation is applied to investigate a cosmological model for a primordial universe that includes a self-interacting bosonic field as source. This model permits, initially, to consider an arbitrary ω function, not usual for BD formulations. The imposition of Noether symmetries conditions identifies a reduced space for the ω function. This model is shown to present a variety of behaviors consistent with a primordial era, depending on the parameters chosen. We find that the bosonic field is capable of promoting a transition from an initially accelerated to a decelerated regime. The self-interaction potential is also restricted by the Noether conditions, and can be interpreted as a vacuum energy contribution. The model also permits a quantization process, going through a hamiltonian formulation and recognizing the presence of cyclic variables. The Bohm approach shows as result a consistent model with a smooth classical limit as the Universe leaves the Planck era.

Impact of star pressure on γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} in modified gravity beyond post-Newtonian approach

We offer a concrete example exhibiting marked departure from the Parametrized Post-Newtonian (PPN) approximation in a modified theory of gravity. Specifically, we derive the exact formula for the Robertson parameter γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} in Brans–Dicke gravity for spherical compact stars, explicitly incorporating the pressure content of the stars. We achieve this by exploiting the integrability of the 00-component of the Brans–Dicke field equation. In place of the conventional PPN result γPPN=ω+1ω+2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _{\\,\ ext {PPN}}=\\frac{\\omega +1}{\\omega +2}$$\\end{document}, we obtain the analytical expression γexact=ω+1+(ω+2)Θω+2+(ω+1)Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _{\\,\ ext {exact}}=\\frac{\\omega +1+(\\omega +2)\\Theta }{\\omega +2+(\\omega +1)\\Theta }$$\\end{document} where Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document} is the ratio of the total pressure P‖∗+2P⊥∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{\\parallel }^{*}+2P_{\\perp }^{*}$$\\end{document} and total energy E∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E^{*}$$\\end{document} contained within the star. The dimensionless quantity Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document} participates in γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} due to the scalar degree of freedom of Brans–Dicke gravity. Our non-perturbative formula is valid for all field strengths and types of matter comprising the star. In addition, we establish two new mathematical identities linking the active gravitational mass, the ADM (Arnowitt–Deser–Misner) mass, and the Tolman mass, applicable for Brans–Dicke gravity. We draw four key conclusions:(1) The usual γPPN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _{\\,\ ext {PPN}}$$\\end{document} formula is violated for high-pressure mass sources, such as neutron stars, viz. when Θ≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta \ e 0$$\\end{document}, revealing a limitation of the PPN approximation in Brans–Dicke gravity. (2) The PPN result mainly stems from the assumption of pressureless matter. Even in the weak-field star case, non-zero pressure leads to a violation of the PPN formula for γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}. Conversely, the PPN result is a good approximation for low-pressure matter, i.e. when Θ≈0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta \\approx 0$$\\end{document}, for all field strengths. (3) Observational constraints on γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} set joint bounds on ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} and Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document}, with the latter representing a global characteristic of a mass source. If the equation of state of matter comprising the mass source approaches the ultra-relativistic form, entailing Θ≃1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta \\simeq 1$$\\end{document}, γexact\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _{\\,\ ext {exact}}$$\\end{document} converges to 1 irrespective of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}. More generally, regardless of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}, ultra-relativistic matter tends to suppress the scalar degree of freedom in the exterior vacuum of Brans–Dicke stars, reducing the vacuum to the Schwarzschild solution. (4) In a broader context, by exposing a limitation of the PPN approximation in Brans–Dicke gravity, our findings indicate the significance of considering the interior structure of stars in observational astronomy when testing candidate theories of gravitation that involve additional degrees of freedom besides the metric tensor.

Chameleon mechanism in scalar nonmetricity cosmology

We investigate the dynamics and the phase-space evolution for the scalar nonmetricity cosmology with a Chameleon mechanism. In particular, we consider a spatially flat Friedmann–Lemaître–Robertson–Walker geometry and within the framework of scalar nonmetricity theory, we consider a generalization of the Brans–Dicke theory in nonmetricity gravity. Introducing a pressureless gas as the matter source, we also incorporate a coupling function responsible for the interaction. Our findings reveal that the choice of connection in nonmetricity gravity significantly impacts the interaction between the scalar field and the matter source. For one particular connection, we discover the absence of asymptotic solutions with a nontrivial interacting component. More precisely, in this scenario, the matter source does not directly interact with the scalar field; however, there is an interaction with the dynamical degrees of freedom provided by the connection.

Test of the Brans–Dicke theory with GW200105 and GW200115

We study whether it is possible to constrain the Brans–Dicke (BD) theory from the measurement of gravitational waves (GW) released in neutron star-black hole collisions. Considering the scalar field modifications through monopole and dipole radiations, we find additional contributions to the phase evolution in the emitted gravitational waveform. After effectively calculating such effect in the post-Newtonian order, we are in a position to measure the scalar field and give bounds on the BD coupling parameter ω BD . We derive the analytical expression for the phase modification due to the orbital eccentricity of eccentric binaries in both general relativity and BD theory. Employing the Bayesian analysis, we obtain the constraints on ω BD from the GW events, GW200105 and GW200115.

Casimir wormholes in Brans–Dicke theory

In recent years there has been a growing interest in the field of wormhole physics in the presence of Casimir effect. As this effect provides negative energy density, it can be utilized as an ideal candidate for the exotic matter required for creating a traversable wormhole. In the context of modified theories of gravity such as Brans–Dicke (BD) theory (Brans and Dicke 1961 Phys. Rev. 124 925), wormhole geometries have been vastly investigated. However, the scientific literature is silent on the issue of BD wormholes in the presence of Casimir energy. Our aim in the present study is to seek for static spherically symmetric solutions representing wormhole configurations in BD theory with Casimir energy as the supporting matter. The Casimir setup we assume comprises two electrically neutral, infinitely large parallel planes placed in a vacuum. We then consider the Casimir vacuum energy density of a scalar field in such a configuration with Dirichlet and mixed boundary conditions. In the former case the corresponding Casimir force is attractive and in the latter this force is repulsive. We present exact zero tidal force wormhole solutions as well as those with non vanishing redshift function for both types of Casimir energies. The conditions on wormhole solutions along with the weak (WEC) and null (NEC) energy conditions put constraints on the values of BD coupling parameter. These constraints are also subject to the value of BD scalar field at the throat and the throat radius. We therefore find that BD wormholes in the presence of Casimir energy can exist without violating NEC and WEC (for the repulsive Casimir force). Finally, we examine the equilibrium condition for stability of the obtained solutions using Tolman–Oppenheimer–Volkoff equation.

Gauss–Bonnet source of Brans–Dicke scalar field and accelerated expansion of universe

In this work, using a different theoretical approach, we study a homogeneous and isotropic cosmological spacetime filled with a perfect fluid. Using the framework of Brans–Dicke (BD) and Gauss–Bonnet (GB) theories and including a scalar potential, we obtain the analytical solution of the field equations and find the field functions and the relevant expansion parameter of the spacetime. We assume that the BD and GB media can interact with each other, and hence that there is an energy transfer between these two components. Using this approach, we assume that the BD scalar field is related to intrinsic properties of the GB medium. We introduced a power-law scalar field [Formula: see text] and found the appropriate dynamical functions for the different powers p. We found that the expansion rate of spacetime also behaves as a power-law, and the accelerating expansion is always satisfied for this model. We also analyze the stability for physically acceptable critical points for a given scale factor.

Cosmological solutions in the Brans–Dicke theory via invariants of symmetry groups

We proceed to obtain an exact analytical solution of the Brans–Dicke (BD) equations for the spatially flat ([Formula: see text]) Friedmann–Lamaître–Robertson–Walker (FLRW) cosmological model in both cases of the absence and presence of the cosmological constant. The solution method that we use to solve the field equations of the BD equations is called the “invariants of symmetry groups method” (ISG method). This method is based on the extended Prelle–Singer (PS) method and it employs the Lie point symmetries, [Formula: see text]-symmetries, and Darboux polynomials (DPs). Indeed, the ISG method tries to provide two independent first-order invariants associated to the one-parameter Lie groups of transformations keeping the ordinary differential equations (ODEs) invariant, as solutions. It should be noted for integrable ODEs that the ISG method guarantees the extraction of these two invariants. In this work, for the BD equations in FLRW cosmological model, we find the Lie point symmetries, [Formula: see text]-symmetries, and DPs, and obtain the basic quantities of the extended PS method (which are the null forms and the integrating factors). By making use of the extended PS method we find two independent first-order invariants in such a way that appropriate cosmological solutions from solving these invariants as a system of algebraic equations are simultaneously obtained. These solutions are wealthy in that they include many known special solutions, such as the O’Hanlon–Tupper vacuum solutions, Nariai’s solutions, Brans–Dicke dust solutions, inflationary solutions, etc.

Anisotropy Bianchi Type-III Cosmological Model in Brans-Dicke Theory of Gravitation

Objectives: To derive the multi-fluid anisotropic Bianchi type-III cosmological model filled with radiation and matter in the presence of Brans-Dicke scalar-tensor theory. Method: In this paper, we have calculated Brans-Dicke field equations in anisotropic Bianchi type -III space times in the presence of matter and radiation which are minimally interacting fields. To obtain the determinate solution of the model, we considered i) the state of the equation , ii) the shear scalar is directly proportional to the expansion scalar i.e., . Also, consider the deceleration parameter, , where with which yields models with constant deceleration parameter. Findings: This solution shows an anisotropic radiation model in Brans-Dicke's theory. Also, it shows accelerated expansion of the universe and transition of the universe from the deceleration phase to the accelerated phase. Novelty: The derived model's many parameters support recent cosmological findings, indicating the model's good discovery. Thus, within the framework of our established model, we are able to comprehend the cosmic development. Keywords: Bianchi type-III, Brans-Dicke theory, Multifluid, Deceleration parameter, Λ CDM

Constraints on Brans-Dicke gravity from neutron star-black hole merger events using higher harmonics

Constraints on Brans-Dicke gravity from neutron star-black hole merger events using higher harmonics