Gravitational radiation, close binary systems, and the Brans-Dicke theory of gravity

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.

Analyzing test particles falling into a Kerr black hole, we study gravitational waves in Brans-Dicke theory of gravity. First we consider a test particle plunging with a constant polar angle into a rotating black hole and calculate the waveform and emitted energy of both scalar and tensor modes of gravitational radiation. We find that the waveform as well as the energy of the scalar gravitational waves weakly depends on the rotation parameter of a black hole $a$ and on the polar angle. Second, using a model of a nonspherical dust shell of test particles falling into a Kerr black hole, we study when the scalar modes dominate. When a black hole is rotating, the tensor modes do not vanish even for a ``spherically symmetric'' shell; instead a slightly oblate shell minimizes their energy but with a nonzero finite value, which depends on the Kerr parameter $a$. As a result, we find that the scalar modes dominate only for highly spherical collapse, but they never exceed the tensor modes unless the Brans-Dicke parameter ${\ensuremath{\omega}}_{\mathrm{BD}}\ensuremath{\lesssim}750$ for $a/M=0.99$ or unless ${\ensuremath{\omega}}_{\mathrm{BD}}\ensuremath{\lesssim}20000$ for $a/M=0.5$, where $M$ is the mass of a black hole. We conclude that the scalar gravitational waves with ${\ensuremath{\omega}}_{\mathrm{BD}}\ensuremath{\lesssim}$ several thousands do not dominate except for very limited situations (observation from the face-on direction of a test particle falling into a Schwarzschild black hole or highly spherical dust shell collapse into a Kerr black hole). Therefore, observation of polarization is also required when we determine the theory of gravity by the observation of gravitational waves.

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.

Neutron stars are born when massive stars run out of their nuclear fuel and undergo gravitational collapse. Neutron stars belong to the most compact objects in the observable Universe. Macroscopic properties of neutron stars like their masses and radii are sensitive to the microscopic properties of the nuclear equation of state of dense matter. The equation of state is determined by the strong interaction among the constituents. The underlying theory is quantum chromodynamics that is, however, highly non-perturbative in the physics regime relevant for neutron stars. Moreover, neutron stars provide an interplay between nuclear physics and astrophysics. Astrophysical observations like the detection of 2 solar mass neutron stars have a major impact on the equation of state. Radii are, however, inherently difficult to measure due to systematic uncertainties. Other observables like the moment of inertia or the tidal deformability present promising alternatives. The double neutron star system PSR J0737-3039 constitutes an outstanding system as it provides the prospect of a moment of inertia measurement for the first time. A new era stated with the pioneering observation of gravitational waves from a binary neutron star merger. The analysis of the gravitational wave signal of GW170817 provides a range for the tidal deformability of typical neutron stars. Moreover, the current NICER mission will provide simultaneous mass-radius measurements. In this thesis, we use state-of-the-art chiral effective field theory interactions to describe the equation of state at nuclear densities. In the high-density regime beyond nuclear saturation density, we use different extrapolation approaches. First, we utilize the established ansatz of piecewise polytropic equations of state which provides a direct parametrization. However, piecewise polytropic equations of state possess unphysical behavior such as discontinuities in the speed of sound. Second, we use a physically motivated parametrization of the speed of sound inside the neutron star from which we derive the equation of state. Both methods allow us to probe the equation of state over a large range of densities. We further impose general constraints on the equation of state such as the requirement of causality at all densities and the support of at least 2 solar mass neutron stars. From the equations of state compatible with the constraints, we determine diverse neutron star observables. We begin with non-rotating neutron stars and focus on their masses and radii. We study correlations among properties of the equation of state at nuclear densities and observables of typical neutron stars. Moreover, we explore the impact of hypothetical, simultaneous measurements of masses and radii of neutron stars on the equation of state. Applying both simple compatibility cuts and the framework of Bayesian statistics, we investigate the sensitivity of the inference on the chosen parametrization of the equation of state. We extend then our considerations to slowly rotating neutron stars and study the moment of inertia. Assuming hypothetical moment of inertia measurements, we determine constraints for the radius of neutron stars and thus the equation of state. In addition, we extend our considerations of isolated neutron stars to binary neutron star systems. In particular, we treat the tidal field of the companion as a small perturbation. This allows us to determine the tidal deformability. By applying higher orders in the metric perturbation, we calculate the quadrupole moment of neutron stars. Although the structure of neutron stars is sensitive to the equation of state, relations between the moment of inertia, the tidal deformability, and the quadrupole moment are remarkably insensitive. We investigate the properties of neutron stars in binary systems and ultimately confront the results of our models with the gravitational wave constraints from a binary neutron star merger.

We investigate how the gravitational field generated by line sources can be characterized in Brans-Dicke theory of gravity. Adapting an approach previously developed by Israel who solved the same problem in general relativity we show that in the Brans-Dicke theory case it is possible to work out the field equations which relate the energy-momentum tensor of the source to the scalar field, the coupling constant $\ensuremath{\omega}$ and the extrinsic curvature of a tube of constant geodesic radius centered on the line in the limit when the radius shrinks to zero. In this new scenario two examples are considered and an account of the Gundlach-Ortiz solution is included. Finally, a brief discussion of how to treat thin shells in Brans-Dicke theory is given.

Based on the new cosmic CMB temperature data from the Planck satellite, the 9 year polarization data from the WMAP, the BAO distance ratio data from the SDSS and 6dF surveys, we place a new constraint on the Brans-Dicke theory. We adopt a parametrization $\zeta=\ln(1+1/\omega})$, where the general relativity (GR) limit corresponds to $\zeta = 0$. We find no evidence of deviation from general relativity. At 95% probability, $-0.00246 < \zeta < 0.00567$, correspondingly, the region $-407.0 < \omega <175.87$ is excluded. If we restrict ourselves to the $\zeta>0$ (i.e. $\omega >0$) case, then the 95% probability interval is $\zeta<0.00549$, corresponding to $\omega> 181.65$. We can also translate this result to a constraint on the variation of gravitational constant, and find the variation rate today as $\dot{G}=-1.42^{+2.48}_{-2.27} \times 10^{-13} $yr$^{-1} $ ($1\sigma$ error bar), the integrated change since the epoch of recombination is $\delta G/G = 0.0104^{+0.0186}_{-0.0067} $ ($1\sigma$ error bar). These limits on the variation of gravitational constant are comparable with the precision of solar system experiments.

Existence check of non-trivial, stationary axisymmetric black hole solutions\nin Brans-Dicke theory of gravity in different direction from those of Penrose,\nThorne and Dykla, and Hawking is performed. Namely, working directly with the\nknown explicit spacetime solutions in Brans-Dicke theory, it is found that\nnon-trivial Kerr-Newman-type black hole solutions different from general\nrelativistic solutions could occur for the generic Brans-Dicke parameter values\n-5/2\\leq \\omega &lt;-3/2. Finally, issues like whether these new black holes carry\nscalar hair and can really arise in nature and if they can, what the associated\nphysical implications would be are discussed carefully.\n

We investigate global textures in Brans-Dicke theory of gravity. The space-time metric and the scalar field generated by a texture are obtained using the weak field approximation. Some effects predicted by Brans-Dicke theory are compared with the corresponding ones predicted by general relativity.

Gravitational waves from compact binary coalescences are valuable for testing theories of gravity in the strong field regime. By measuring neutron star tidal deformability using gravitational waves from binary neutron stars, stringent constraints were placed on the equation of state of matter at extreme densities. Tidal Love numbers in alternative theories of gravity may differ significantly from their general relativistic counterparts. Understanding exactly how the tidal Love numbers change will enable scientists to untangle physics beyond general relativity from the uncertainty in the equation of state measurement. In this work, we explicitly calculate the fully relativistic l ≥ 2 tidal Love numbers for neutron stars in scalar-tensor theories of gravitation. We use several realistic equations of state to explore how the mass, radius, and tidal deformability relations differ from those of general relativity. We find that tidal Love numbers and tidal deformabilities can differ significantly from those in general relativity in certain regimes. The electric tidal deformability can differ by ∼200%, and the magnetic tidal deformability differs by ∼300%. These deviations occur at large compactnesses (C = M/r ≳ 0.2) and vary slightly depending on the equation of state. This difference suggests that using the tidal Love numbers from general relativity could lead to significant errors in tests of general relativity using the gravitational waves from binary neutron star and neutron star black hole mergers.

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.

In this work it is shown that the Brans-Dicke theory of gravity does not always go over to general relativity in the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\alpha}$ limit. It is also shown, by an order of magnitude estimate, that one can get general relativity as a limit of Brans-Dicke theory when $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\alpha},$ only if the trace of the energy-momentum tensor describing all fields other than the Brans-Dicke scalar field is nonzero.

Three-dimensional simulations for the merger of binary neutron stars are performed in the framework of full general relativity. We pay particular attention to the black hole formation case and to the resulting mass of the surrounding disk for exploring the possibility for formation of the central engine of short-duration gamma-ray bursts (SGRBs). Hybrid equations of state are adopted mimicking realistic, stiff nuclear equations of state (EOSs), for which the maximum allowed gravitational mass of cold and spherical neutron stars, ${M}_{\mathrm{sph}}$, is larger than $2{M}_{\ensuremath{\bigodot}}$. Such stiff EOSs are adopted motivated by the recent possible discovery of a heavy neutron star of mass $\ensuremath{\sim}2.1\ifmmode\pm\else\textpm\fi{}0.2{M}_{\ensuremath{\bigodot}}$. For the simulations, we focus on binary neutron stars of the ADM mass $M\ensuremath{\gtrsim}2.6{M}_{\ensuremath{\bigodot}}$. For an ADM mass larger than the threshold mass ${M}_{\mathrm{thr}}$, the merger results in prompt formation of a black hole irrespective of the mass ratio ${Q}_{M}$ with $0.65\ensuremath{\lesssim}{Q}_{M}\ensuremath{\le}1$. The value of ${M}_{\mathrm{thr}}$ depends on the EOSs and is approximately written as $1.3--1.35{M}_{\mathrm{sph}}$ for the chosen EOSs. For the black hole formation case, we evolve the space-time using a black hole excision technique and determine the mass of a quasistationary disk surrounding the black hole. The disk mass steeply increases with decreasing the value of ${Q}_{M}$ for given ADM mass and EOS. This suggests that a merger with small value of ${Q}_{M}$ is a candidate for producing central engine of SGRBs. For $M&lt;{M}_{\mathrm{thr}}$, the outcome is a hypermassive neutron star of a large ellipticity. Because of the nonaxisymmetry, angular momentum is transported outward. If the hypermassive neutron star collapses to a black hole after the long-term angular momentum transport, the disk mass may be $\ensuremath{\gtrsim}0.01{M}_{\ensuremath{\bigodot}}$ irrespective of ${Q}_{M}$. Gravitational waves are computed in terms of a gauge-invariant wave extraction technique. In the formation of the hypermassive neutron star, quasiperiodic gravitational waves of frequency between 3 and 3.5 kHz are emitted irrespective of EOSs. The effective amplitude of gravitational waves can be $\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ at a distance of 50 Mpc, and hence, it may be detected by advanced laser-interferometers. For the black hole formation case, the black hole excision technique enables a long-term computation and extraction of ring-down gravitational waves associated with a black hole quasinormal mode. It is found that the frequency and amplitude are $\ensuremath{\approx}6.5--7\text{ }\text{ }\mathrm{kHz}$ and $\ensuremath{\sim}{10}^{\ensuremath{-}22}$ at a distance of 50 Mpc for the binary of mass $M\ensuremath{\approx}2.7--2.9{M}_{\ensuremath{\bigodot}}$.

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.

Gravitational radiation and the binary pulsar

Scalar-tensor gravity, exemplified by Brans-Dicke (BD) gravity, introduces additional scalar polarization modes that contribute scalar radiation alongside tensor modes.We conduct a comprehensive analysis of how gravitational wave generation and propagation effects under Brans-Dicke gravity are encoded into the astrophysical stochastic gravitational wave background (AGWB).We perform end-to-end analyses of realistic populations of simulated coalescing binary systems to generate AGWB mock data with third-generation gravitational wave detectors and conducted a complete Bayesian analysis for the first time.We find the uncertainties in the population properties of binary black holes (BBH) significantly affect the ability to constrain BD gravity.Furthermore, we explore the detectability of potential scalar backgrounds that originates from binary neutron star (BNS) and neutron-star-black-hole (NSBH) mergers, with NSBH systems expected to modify the spectral index of the scalar background and introduce oscillatory behavior.We show that the observations of the AGWB enable the separation of mixed tensor and scalar polarization modes with comparable sensitivity to each mode.However, the scalar background is expected to remain substantially weaker than the tensor background, even in scenarios where BD gravity exhibits significant deviations from general relativity (GR), resulting only upper limits can be placed on the scalar background.We conclude that for ambiguous populations, employing waveform matching with individual sources provides a more robust approach to constrain BD gravity.