Brans-Dicke Coupling Parameter Research Articles

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.

Constraint on Brans-Dicke theory from intermediate/extreme mass ratio inspirals

Intermediate/Extreme mass ratio inspiral (I/EMRI) system provides a good toolto test the nature of gravity in strong field.Based on the method of osculating orbits,we compute the orbital evolutions of I/EMRIs on quasi-elliptic orbits inboth Einstein's general relativity and Brans-Dicke theory.The extra monopolar and dipolar channels in Brans-Dicke theory accelerate the orbital decay,so it is important to consider the effects of monopolar and dipolar emissions on the waveform.With the help of accurate orbital motion,we generate waveform templates which include both monopolar and dipolar contributions for I/EMRIs on eccentric orbits in Brans-Dicke theory.With a two-year observation of gravitational waves emitted from I/EMRIs by LISA,we get the most stringent constraint on the Brans-Dicke coupling parameter ω 0 > 106.

Constraining gravity with eccentric gravitational waves: projected upper bounds and model selection

Gravitational waves allow us to test general relativity in the highly dynamical regime. While current observations have been consistent with waves emitted by quasi-circular binaries, eccentric binaries may also produce detectable signals in the near future with ground- and space-based detectors. We here explore how tests of general relativity scale with the orbital eccentricity of the source during the inspiral of compact objects up to e ∼ 0.8. We use a new, third post-Newtonian-accurate, eccentric waveform model for the inspiral of compact objects, which is fast enough for Bayesian parameter estimation and model selection, and highly accurate for modeling moderately eccentric inspirals. We derive and incorporate the eccentric corrections to this model induced in Brans–Dicke theory and in Einstein–dilaton–Gauss–Bonnet gravity at leading post-Newtonian order, which suggest a straightforward eccentric extension of the parameterized post-Einsteinian formalism. We explore the upper limits that could be set on the coupling parameters of these modified theories through both a confidence-interval- and Bayes-factor-based approach, using a Markov-Chain Monte Carlo and a trans-dimensional, reversible-jump, Markov-Chain Monte Carlo method. We find projected constraints with signals from sources with e ∼ 0.4 that are one order of magnitude stronger than that those obtained with quasi-circular binaries in advanced LIGO. In particular, eccentric gravitational waves detected at design sensitivity should be able to constrain the Brans–Dicke coupling parameter ω ≳ 3300 and the Gauss–Bonnet coupling parameter α1/2 ≲ 0.5 km at 90% confidence. Although the projected constraint on ω is weaker than other current constraints, the projected constraint on α1/2 is 10 times stronger than the current gravitational wave bound.

Improved constraints on modified gravity with eccentric gravitational waves

Recent gravitational wave observations have allowed stringent new constraints on modifications to General Relativity (GR) in the extreme gravity regime. Although these observations were consistent with compact binaries with no orbital eccentricity, gravitational waves emitted in mildly eccentric binaries may be observed once detectors reach their design sensitivity. In this paper, we study the effect of eccentricity in gravitational wave constraints of modified gravity, focusing on Jordan-Brans- Dicke-Fierz theory as an example. Using the stationary phase approximation and the post-circular approximation (an expansion in small eccentricity), we first construct an analytical expression for frequency-domain gravitational waveforms produced by inspiraling compact binaries with small eccentricity in this theory. We then calculate the overlap between our approximate analytical waveforms and an eccentric numerical model (TaylorT4) to determine the regime of validity (in eccentricity) of the former. With this at hand, we carry out a Fisher analysis to determine the accuracy to which Jordan-Brans-Dicke-Fierz theory could be constrained given future eccentric detections consistent with General Relativity. We find that the constraint on the theory initially deteriorates (due to covariances between the eccentricity and the Brans-Dicke coupling parameter), but then it begins to recover, once the eccentricity is larger than approximately 0.03. We also find that third-generation ground-based detectors and space-based detectors could allow for constraints that are up to an order of magnitude more stringent than current Solar System bounds. Our results suggest that waveforms in modified gravity for systems with moderate eccentricity should be developed to maximize the theoretical physics that can be extracted in the future.

Kinetic inflation in deformed phase space Brans–Dicke cosmology

In this paper, by establishing a Brans-Dicke (BD) cosmology by means of a deformed phase space, in the absence of any scalar potential, cosmological constant and ordinary matter, we show that it is feasible to overcome obstacles reported in the corresponding commutative (non-deformed) frameworks. More concretely, by applying the Hamiltonian formalism and introducing a dynamical deformation, between the momenta associated to the FLRW scale factor and the BD scalar field, we obtain the modified equations of motion. In particular, these equations reduce to their standard counterparts when the noncommutative (NC) parameter is switched off. By focusing on a specific branch of solutions, in contrast to standard frameworks (even with a varying BD coupling parameter), we show that we can obtain an adequate appropriate inflationary epoch possessing a suitable graceful exit. In other words, in the Jordan frame (JF), such branch of solutions properly satisfy the sufficient condition required for satisfactory inflation, which is equivalent to get an inflationary phase in the conformal Einstein frame (EF) without branch change. Concerning the cosmological dynamics, we further show that our NC framework bears close resemblance to the $R^2$ (Starobinsky) inflationary model.

Generalized Brans-Dicke theory: A dynamical systems analysis

The stability criteria for the generalized Brans-Dicke cosmology in a spatially flat, homogeneous and isotropic cosmological model is discussed in the presence of a perfect fluid. The generalization comes through the channel that the Brans-Dicke coupling parameter $\omega$ is allowed to be a function of the scalar field $\phi$. This generalization can lead to a host of scalar-tensor theories of gravity for various choices of $\omega = \omega (\phi)$. A very interesting general result has been found. Excepting for the case of a radiation distribution as the choice of the fluid, all other solutions find a natural habitat in the corresponding solutions in general relativity in an infinite $\omega$ limit. For the radiation distribution, the dependence of stability on $\omega$ is a bit obscure. If a scalar potential, function of the Brans-Dicke scalar field, is added to the action, the requirement of an infinite $\omega$ for stability is relaxed for a matter distribution with a non-zero trace whereas it becomes a possibility for a radiation distribution.

Non-singular Brans–Dicke collapse in deformed phase space

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.

Trapped surfaces and the nature of singularity in Lyraʼs geometry

Motivated by the geometrical interpretation of the Brans–Dicke (BD) scalar field, which may also act as a torsion potential in Lyra geometry, we study the effects of spacetime torsion on the dynamics of a collapsing massive star. Taking the interior spacetime as the FLRW metric and the matter content as spherically symmetric, homogeneous perfect fluid with the equation of state (EoS) , we show that the collapse ends in a spacetime singularity which is of a strong curvature type in the sense of Tipler. Whether the trapped surfaces form during the dynamical evolution of the collapse depends on the torsion parameter, related to the BD coupling parameter, and the EoS subject to the conditions of the physical reasonableness of the collapse configuration. Hence, the space of the torsion and EoS parameters is divided into two portions, one for which the collapse process leads to the formation of the apparent horizon, and the other for which the apparent horizon fails to form in the interior region. The nature of the singularity is examined from the exterior perspective by searching for the existence of radial null geodesics reaching the faraway observers. Moreover, it is found that the effects of a dynamical torsion can be transferred to the outside region of the collapsing star, making the exterior region dynamic.

Gravitational radiation from compact binary systems in the massive Brans-Dicke theory of gravity

We derive the equations of motion, the periastron shift, and the gravitational radiation damping for quasicircular compact binaries in a massive variant of the Brans-Dicke theory of gravity. We also study the Shapiro time delay and the Nordtvedt effect in this theory. By comparing with recent observational data, we put bounds on the two parameters of the theory: the Brans-Dicke coupling parameter \omega_{BD} and the scalar mass m_s. We find that the most stringent bounds come from Cassini measurements of the Shapiro time delay in the Solar System, that yield a lower bound \omega_{BD}>40000 for scalar masses m_s<2.5x10^{-20} eV, to 95% confidence. In comparison, observations of the Nordtvedt effect using Lunar Laser Ranging (LLR) experiments yield \omega_{BD}>1000 for m_s<2.5x10^{-20} eV. Observations of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR J1012+5307 yield \omega_{BD}>1250 for m_s<10^{-20} eV. A first estimate suggests that bounds comparable to the Shapiro time delay may come from observations of radiation damping in the eccentric white dwarf-neutron star binary PSR J1141-6545, but a quantitative prediction requires the extension of our work to eccentric orbits.

Composite vacuum Brans-Dicke wormholes

We construct a new static spherically symmetric configuration composed of interior and exterior Brans-Dicke vacua matched at a thin matter shell. Both vacua correspond to the same Brans-Dicke coupling parameter $\omega$, however they are described by the Brans class I solution with different sets of parameters of integration. In particular, the exterior vacuum solution has $C_{ext}(\omega)\equiv 0$. In this case the Brans class I solution for any $\omega$ reduces to the Schwarzschild one being consistent with restrictions on the post-Newtonian parameters following from recent Cassini data. The interior region possesses a strong gravitational field, and so the interior vacuum solution has $C_{int}(\omega)=-1/(\omega+2)$. In this case the Brans class I solution describes a wormhole spacetime provided $\omega$ lies in the narrow interval $-2-\frac{\sqrt{3}}{3}<\omega<-2$. The interior and exterior regions are matched at a thin shell made from an ordinary perfect fluid with positive energy density and pressure obeying the barotropic equation of state $p=k\sigma$ with $0\le k\le1$. The resulting configuration represents a composite wormhole, i.e. the thin matter shell with the Schwarzschild-like exterior region and the interior region containing the wormhole throat.

STUDY OF SYMMETRY IN F(R) THEORY OF GRAVITY

An action in which the Ricci scalar is non-minimally coupled with a scalar field and contains higher order curvature invariant terms carries a conserved current under certain conditions that decouples geometric part from the scalar field. The conserved current relates the pair of arbitrary coupling parameters f(ϕ) and ω(ϕ) with the gravitational field variable, where ω(ϕ) is the Brans–Dicke coupling parameter. The existence of such conserved current may be helpful to sketch the cosmological evolution from its early age till date in a single frame.

Scalar–tensor theory of gravity carrying a conserved current

A general scalar–tensor theory of gravity carries a conserved current for a trace-free minimally coupled scalar field, under the condition that the potential V(ϕ) of the non-minimally coupled scalar field is proportional to the square of the parameter f(ϕ) that is coupled with the scalar curvature R. The conserved current relates the pair of arbitrary coupling parameters f(ϕ) and ω(ϕ) with the gravitational field variable, where ω(ϕ) is the Brans–Dicke coupling parameter. Thus fixing up the two arbitrary parameters by hand, it is possible to explore the symmetries and the form of conserved currents corresponding to standard and many different nonstandard models of gravity. To demonstrate how the presence of conserved current makes it easier to tackle the field equations a couple of homogeneous cosmological solutions are presented. Modification of such a general scalar–tensor theory of gravity with the introduction of higher-order curvature-invariant terms also admits the same conserved current, though under a different condition.

GRAVITATIONAL WAVES IN GENERALISED BRANS–DICKE THEORY

We have solved cosmological gravitational wave (GW) equation in the framework of generalised Brans–Dicke (GBD) theory for all epochs of the Universe. The solutions are expressed in terms of the present value ω0 of the Brans–Dicke coupling parameter. We also obtain the constraints on ω0 for the solutions to represent growing modes in different epochs.

SELF INTERACTING BRANS–DICKE COSMOLOGY AND QUINTESSENCE

Recent cosmological observations reveal that we are living in a flat accelerated expanding universe. In this work we have investigated the nature of the potential compatible with the power law expansion of the universe in a self interacting Brans–Dicke cosmology with a perfect fluid background and have analyzed whether this potential supports the accelerated expansion. It is found that positive power law potential is relevant in this scenario and can drive accelerated expansion for negative Brans–Dicke coupling parameter ω. The evolution of the density perturbation is also analyzed in this scenario and is seen that the model allows growing modes for negative ω.

Testing scalar-tensor gravity using space gravitational-wave interferometers

We calculate the bounds which could be placed on scalar-tensor theories of gravity of the Jordan, Fierz, Brans and Dicke type by measurements of gravitational waveforms from neutron stars (NS) spiraling into massive black holes (MBH) using LISA, the proposed space laser interferometric observatory. Such observations may yield significantly more stringent bounds on the Brans-Dicke coupling parameter $\ensuremath{\omega}$ than are achievable from solar system or binary pulsar measurements. For NS-MBH inspirals, dipole gravitational radiation modifies the inspiral and generates an additional contribution to the phase evolution of the emitted gravitational waveform. Bounds on $\ensuremath{\omega}$ can therefore be found by using the technique of matched filtering. We compute the Fisher information matrix for a waveform accurate to second post-Newtonian order, including the effect of dipole radiation, filtered using a currently modeled noise curve for LISA, and determine the bounds on $\ensuremath{\omega}$ for several different NS-MBH canonical systems. For example, observations of a ${1.4M}_{\ensuremath{\bigodot}}$ NS inspiraling to a ${10}^{3}{M}_{\ensuremath{\bigodot}}$ MBH with a signal-to-noise ratio of 10 could yield a bound of $\ensuremath{\omega}&gt;240000,$ substantialy greater than the current experimental bound of $\ensuremath{\omega}&gt;3000.$

Brans-Dicke corrections to the gravitational Sagnac effect

The {\it exact} formulation for the effect of the Brans-Dicke scalar field on the gravitational corrections to the Sagnac delay in the Jordan and Einstein frames is presented for the first time. The results completely agree with the known PPN factors in the weak field region. The calculations also reveal how the Brans-Dicke coupling parameter (appears in various correction terms for different types of source/observer orbits. A first order correction of roughly 2.83 x 10^{-1} fringe shift for visible light is introduced by the gravity-scalar field combination for Earth bound equatorial orbits. It is also demonstrated that the final predictions in the two frames do not differ. The effect of the scalar field on the geodetic and Lense-Thirring precession of a spherical gyroscope in circular polar orbit around the Earth is also computed with an eye towards the Stanford Gravity Probe-B experiment currently in progress. The feasibility of optical and matter-wave interferometric measurements is discussed briefly.

BD-FRW Cosmology with Bulk Viscosity

Exact cosmological solutions of the field equations in Brans-Dicke (BD) theory, with k = 0, FRW metric have been obtained in the presence of bulk viscosity. It is found that constant bulk viscosity leads to an inflationary solution for large values of the BD coupling parameter w. The case of radiative bulk viscosity during the decoupling era is investigated and the production of entropy is estimated.