Scalar Gravitational Waves Research Articles

GR 20 parallel session A3: modified gravity

The parallel session (A3), on “Modified Gravity”, enjoyed one on the largest number of abstract submissions (over 80), resulting in the selection of 24 oral presentations. The three short papers presented in the following sections are based on the session talks by Arif Mohd on thermodynamics of universal horizons in Einstein-Æther theory, Conformal anomalies in Hořava-Lifshitz gravity by Charles Melby-Thompson and detectability of scalar gravitational waves by LIGO and Virgo by Peter Shawhan. They have been selected as a representative sample, to illustrate some of the best in the remarkable and encouraging variety of topics discussed in the session—ranging from highly theoretical, to phenomenological, observational, and experimental—with all these areas playing an integral part in our quest to understand the limits of standard general relativity.

Scalar gravitational waves from relativistic stars in scalar-tensor gravity

Unlike general relativity, the scalar gravitational waves can be excited due to the radial oscillations in scalar-tensor gravity. To examine the scalar gravitational waves in scalar-tensor gravity, we derive the evolution equations of the radial oscillations of neutron stars and determine the specific oscillation frequencies of the matter oscillations and scalar gravitational waves, where we adopt two different numerical approaches, i.e., the mode analysis and direct time evolution. As a result, we observe the spontaneous scalarization even in the radial oscillations. Depending on the background scalar field and coupling constant, the total energy radiated by the scalar gravitational waves dramatically changes, where the specific oscillation frequencies are completely same as the matter oscillations. That is, via the direct observations of scalar gravitational waves, one can not only reveal the gravitational theory, but also extract the radial oscillations of neutron stars.

The LIGO–LIGO cross correlation for the detection of relic scalar gravitational waves

In an earlier work we studied the cross correlation between the Virgo interferometer and the MiniGRAIL resonant sphere for the detection of relic scalar gravitational waves (SGWs). We have shown that the overlap reduction function for the cross correlation between Virgo and the monopole mode of MiniGRAIL is very small, but a maximum was also found in the correlation at about 2710Hz, in the range of the MiniGRAIL sensitivity.In this paper the analysis is improved. After carefully reviewing the response function of interferometers to SGWs directly in the gauge of the local observer, the result is used to analyze the cross correlation between the two LIGO interferometers in their advanced configuration for a potential detection of relic SGWs and to release a lower bound for the integration time of such a detection. By using a new, frequency-dependent, overlap reduction function, a comparison with previous low-frequency approximations is therefore discussed.This is the first time that such a cross-correlation is computed in all the frequency spectrum of relic SGWs. The computation of a better signal to noise ratio is very important to understand if a scalar component of GWs is present at high frequency. With the new overlap reduction function, an order of magnitude is gained concerning the integration time for detecting the relic SGWs’ signal. This could be very important for a potential detection if advanced projects further improve their sensitivity.

Parametric instability induced scalar gravitational waves from a model pulsating neutron star

We identify a new dynamical mechanism for a strong scalar gravitational field effect. To illustrate this mechanism, we investigate the parametric excitation and emission of scalar gravitational waves by a radially pulsating model neutron star.

Testing metric-affine f(R)-gravity by relic scalar gravitational waves

We discuss the emergence of scalar gravitational waves in metric-affine f(R)-gravity. Such a component allows to discriminate between metric and metric-affine theories The intrinsic meaning of this result is that the geodesic structure of the theory can be discriminated. We extend the formalism of cross-correlation analysis, including the additional polarization mode, and calculate the detectable energy density of the spectrum for cosmological relic gravitons. The possible detection of the signal is discussed against the sensitivities of the VIRGO, LIGO and LISA interferometers.

Stochastic Background of Relic Scalar Gravitational Waves tuned by Extended Gravity

A stochastic background of relic gravitational waves is achieved by the so called adiabatically-amplified zero-point fluctuations process derived from early inflation. It provides a distinctive spectrum of relic gravitational waves. In the framework of scalar-tensor gravity, we discuss the scalar modes of gravitational waves and the primordial production of this scalar component which is generated beside tensorial one. Then we analyze different viable $f(R)$-gravities towards the Solar System tests and stochastic gravitational waves background. The aim is to achive experimental bounds for the theory at local and cosmological scales in order to select models capable of addressing the accelerating cosmological expansion without cosmological constant but evading the weak field constraints. It is demonstrated that viable $f(R)$-gravities under consideration not only satisfy the local tests, but additionally, pass the PPN-and stochastic gravitational waves bounds for large classes of parameters.

Position and frequency shifts induced by massive modes of the gravitational wave background in alternative gravity

Alternative theories of gravity predict the presence of massive scalar, vector, and tensor gravitational wave modes in addition to the standard massless spin 2 graviton of general relativity. The deflection and frequency shift effects on light from distant sources propagating through a stochastic background of gravitational waves, containing such modes, differ from their counterparts in general relativity. Such effects are considered as a possible signature for alternative gravity in attempts to detect deviations from Einstein's gravity by astrophysical means.

Wormhole Perturbation and Its Quasi Normal Modes

In this paper, we study the perturbation problems for the cases of the scalar, electromagnetic, and axial gravitational waves under the traversable Lorentzian wormhole geometry.

The initial value problem of scalar-tensor theories of gravity

The initial value problem of scalar-tensor theories of gravity (STT) is analyzed in the physical (Jordan) frame using a 3+1 decomposition of spacetime. A first order strongly hyperbolic system is obtained for which the well posedness of the Cauchy problem can be established. We provide two simple applications of the 3+1 system of equations: one for static and spherically symmetric spacetimes which allows the construction of unstable initial data (compact objects) for which a further black hole formation and scalar gravitational wave emission can be analyzed, and another application is for homogeneous and isotropic spacetimes that permits to study the dynamics of the Universe in the framework of STT.

THE VIRGO–MINIGRAIL CROSS CORRELATION FOR THE DETECTION OF SCALAR GRAVITATIONAL WAVES

After a review of the frequency-dependent angular pattern of interferometers in the TT gauge for scalar gravitational waves (SGWs), which has been recently analysed by Capozziello and Corda, in this letter the result is used to study the cross correlation between the Virgo interferometer and the MiniGRAIL resonant sphere. It is shown that the overlap reduction function for the cross correlation between Virgo and the monopole mode of MiniGRAIL is very small, but a maximum is also found in the correlation at about 2710 Hz, in the range of the MiniGRAIL sensitivity.

The production of matter from curvature in a particular linearized high order theory ofgravity and the longitudinal response function of interferometers

The strict analogy between scalar–tensor theories of gravity and high order gravity iswell known in the literature. In this paper it is shown that, from a particularhigh order gravity theory known in the literature, it is possible to produce, inthe linearized approach, particles which can be seen like massive scalar modesof gravitational waves, and the response of interferometers to such particles isanalysed. The presence of the mass generates a longitudinal force in addition of thetransverse one which is appropriate to the massless gravitational waves and theresponse of an arm of an interferometer to this longitudinal effect in the frameof a local observer is computed. This longitudinal response function is directlyconnected to the function of the Ricci scalar in the particular action of this highorder theory. Important consequences from a theoretical point of view could arisefrom this approach, because it opens up the possibility of using the signals seenfrom interferometers to understand which is the correct theory of gravitation.The presence of the mass could also have important applications in cosmology because ofthe fact that gravitational waves can have mass and could give a contribution to the darkmatter of the Universe.

Quasi-isotropic solution of the Einstein equations neara cosmological singularity for a two-fluid cosmological model

The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion inthe synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized to the case of a two-fluid cosmological model. This solution describes non-decreasing modes of adiabatic and isocurvature scalar perturbations and gravitational waves in the regime when deviations of a spacetime metric from the homogeneous isotropic Friedmann–Robertson–Walker (FRW) background are large while locally measurable quantities like Riemann tensor components are still close to their FRW values. The general structure of the perturbation series is presented and the first coefficients of the series expansion for the metric tensor and the fluid energy densities and velocities are calculated explicitly.

Exact Solution in Chaotic Inflation Model with Potential Minima

Taking the cosmological expansion rate directly as a function of field , we present a new exact solution to Einstein's equations that describe the evolution of cosmological chaotic inflation model. The inflation is driven by the evolution of scalar field with inflation potential . The spectral indices of the scalar density and gravitational wave fluctuations are computed. The value of lies well inside the limits set by the cosmic background explorer satellite.

Statistics of the detection rates for tensor and scalar gravitational waves from the Local Galaxy universe

We use data on the local 3-dimensional galaxy distribution for studying the statistics of the detection rates of gravitational waves (GW) coming from supernova explosions. We consider both tensor and scalar grav- itational waves which are possible in a wide range of relativistic and quantum gravity theories. We show that statistics of GW events as a function of sidereal time can be used for distinction between scalar and tensor gravi- tational waves because of the anisotropy of spatial galaxy distribution. For calculation of the expected amplitudes of GW signals we use the values of the released GW energy, frequency and duration of GW pulse which are consistent with existing scenarios of SN core collapse. The amplitudes of the signals produced by Virgo and the Great Attractor clusters of galaxies is expressed as a function of the sidereal time for resonant bar detectors oper- ating now (IGEC) and for forthcoming laser interferometric detectors (VIRGO). Then, we calculate the expected number of GW events as a function of sidereal time produced by all the galaxies within 100 Mpc. In the case of axisymmetric rotational core collapse which radiates a GW energy of 10 9 Mc 2 , only the closest explosions can be detected. However, in the case of nonaxisymmetric supernova explosion, due to such phenomena as centrifugal hangup, bar and lump formation, the GW radiation could be as strong as that from a coalescing neutron-star binary. For radiated GW energy higher than 10 6 Mc 2 and sensitivity of detectors at the level h 10 23 it is possible to detect Virgo cluster and Great Attractor, and hence to use the statistics of GW events for testing gravity theories.

Response of interferometric detectors to scalar gravitational waves

We rigorously analyze the frequency response functions and antenna sensitivity patterns of three types of interferometric detectors to the scalar mode of gravitational waves which is predicted to exist in the scalar-tensor theory of gravity. By a straightforward treatment, we show that the antenna sensitivity pattern of the simple Michelson interferometric detector depends strongly on the wavelength ${\ensuremath{\lambda}}_{\mathrm{SGW}}$ of the scalar mode of the gravitational waves if ${\ensuremath{\lambda}}_{\mathrm{SGW}}$ is comparable to an arms length of the interferometric detector. For the Delay-Line and Fabry-Perot interferometric detectors with an arms length much shorter than ${\ensuremath{\lambda}}_{\mathrm{SGW}},$ however, the antenna sensitivity patterns depend weakly on ${\ensuremath{\lambda}}_{\mathrm{SGW}}$ even though ${\ensuremath{\lambda}}_{\mathrm{SGW}}$ is comparable to the effective path length of those interferometers. This agrees with the result obtained by Maggiore and Nicolis.

Dilaton gravity on the brane

We derive the four-dimensional field equations for the induced metric and scalar field on the world-volume of a 3-brane in a five-dimensional bulk with Einstein gravity plus a self-interacting scalar field. We calculate the effective four-dimensional gravitational constant and cosmological constant for arbitrary forms of the brane tension and self-interaction potential for the scalar field in the bulk. In addition to the canonical energy-momentum tensor for the scalar field and ordinary matter on the brane, the effective four-dimensional Einstein equations include terms due to the scalar field and gravitational waves in the bulk. We present solutions corresponding to static Minkowski brane worlds and also dynamical Friedmann-Robertson-Walker brane world cosmologies. We discuss the induced coupling of the scalar field to ordinary matter on the brane.

Do gravitational wavescreate particles?

Solving the Klein-Gordon equation for a free scalar field in a curvedspacetime in the weak-field approximation we rederive the results ofGibbons et al: no particle creation from theinteraction between scalar fields and gravitational waves. We show,however, that particle creation would really occur when the matter fieldis constrained in space by some boundaries. Such an effect is likely to berelated to the uncertainty principle, in connection with a sort of dimensional reduction (as in the Kaluza-Klein theory) that causes thefield to acquire a mass term, also responsible for conformalsymmetry breaking in a spatially flat FRW spacetime. Although derived inthe weak-field approximation, the results seem also to be reasonablyvalid in the presence of exact gravitational waves.

Detection of scalar gravitational waves with a hollow spherical antenna

We study the response and cross sections for the absorption of GW energy generated in a Jordan-Brans-Dicke theory by a resonant mass detector shaped as a hollow sphere. As a source of the GW we take a binary system in the Newtonian approximation. For masses of the stars of the order of the solar mass, the emitted GW sweeps a range of frequencies which include the first resonant mode of the detector.

Detection strategies for scalar gravitational waves with interferometers and resonant spheres

We compute the response and the angular pattern function of an interferometer for a scalar component of gravitational radiation in Brans-Dicke theory. We examine the problem of detecting a stochastic background of scalar GWs and compute the scalar overlap reduction function in the correlation between an interferometer and the monopole mode of a resonant sphere. While the correlation between two interferometers is maximized taking them as close as possible, the interferometer-sphere correlation is maximized at a finite value of f*d, where `f' is the resonance frequency of the sphere and `d' the distance between the detectors. This defines an optimal resonance frequency of the sphere as a function of the distance. For the correlation between the Virgo interferometer located near Pisa and a sphere located in Frascati, near Rome, we find an optimal resonance frequency f=590 Hz. We also briefly discuss the difficulties in applying this analysis to the dilaton and moduli fields predicted by string theory.

Cross section of a resonant-mass detector for scalar gravitational waves

Gravitationally coupled scalar fields, originally introduced by Jordan, Brans and Dicke to account for a non constant gravitational coupling, are a prediction of many non-Einsteinian theories of gravity not excluding perturbative formulations of String Theory. In this paper, we compute the cross sections for scattering and absorption of scalar and tensor gravitational waves by a resonant-mass detector in the framework of the Jordan-Brans-Dicke theory. The results are then specialized to the case of a detector of spherical shape and shown to reproduce those obtained in General Relativity in a certain limit. Eventually we discuss the potential detectability of scalar waves emitted in a spherically symmetric gravitational collapse.