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We rigorously analyze the frequency response functions and antenna sensitivity patterns of three types of interferometric detectors to 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 wave length $lambda_{rm SGW}$ of the scalar mode of gravitational waves if $lambda_{rm SGW}$ is comparable to the arm length of the interferometric detector. For the Delay-Line and Fabry-Perot interferometric detectors with arm length much shorter than $lambda_{rm SGW}$, however, the antenna sensitivity patterns depend weakly on $lambda_{rm SGW}$ even though $lambda_{rm SGW}$ is comparable to the effective path length of those interferometers. This agrees with the result obtained by Maggiore and Nicolis.
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Gravitational waves are perturbations of the metric of space-time. Six polarizations are possible, although general relativity predicts that only two such polarizations, tensor plus and tensor cross are present for gravitational waves. We give the analytical formulas for the antenna response functions for the six polarizations which are valid for any equal-arm interferometric gravitational-wave detectors without optical cavities in the arms.The response function averaged over the source direction and polarization angle decreases at high frequencies which deteriorates the signal-to-noise ratio registered in the detector. At high frequencies, the averaged response functions for the tensor and breathing modes fall of as $1/f^2$, the averaged response function for the longitudinal mode falls off as $1/f$ and the averaged response function for the vector mode falls off as $ln(f)/f^2$.
We formulate the data analysis problem for the detection of the Newtonian waveform from an inspiraling compact-binary by a network of arbitrarily oriented and arbitrarily distributed laser interferometric gravitational wave detectors. We obtain for the first time the relation between the optimal statistic and the magnitude of the network correlation vector, which is constructed from the matched network-filter. This generalizes the calculation reported in an earlier work (gr-qc/9906064), where the detectors are taken to be coincident.
General metric theories in a four-dimensional spacetime allow at most six polarization states (two spin-0, two spin-1 and two spin-2) of gravitational waves (GWs). If a sky location of a GW source with the electromagnetic counterpart satisfies a single equation that we propose in this paper, both the spin-1 modes and spin-2 ones can be eliminated from a certain combination of strain outputs at four ground-based GW interferometers (e.g. a network of aLIGO-Hanford, aLIGO-Livingston, Virgo and KAGRA), where this equation describes curves on the celestial sphere. This means that, if a GW source is found in the curve (or its neighborhood practically), a direct test of scalar (spin-0) modes separately from the other (vector and tensor) modes become possible in principle. The possibility of such a direct test is thus higher than an earlier expectation (Hagihara et al. PRD, 100, 064010, 2019), in which they argued that the vector modes could not be completely eliminated. We discuss also that adding the planned LIGO-India detector as a fifth detector will increase the feasibility of scalar polarization tests.
In this talk I review recent progresses in the detection of scalar gravitational waves. Furthermore, in the framework of the Jordan-Brans-Dicke theory, I compute the signal to noise ratio for a resonant mass detector of spherical shape and for binary sources and collapsing stars. Finally I compare these results with those obtained from laser interferometers and from Einsteinian gravity.
The renewed serious interest to possible practical applications of gravitational waves is encouraging. Building on previous work, I am arguing that the strong variable electromagnetic fields are appropriate systems for the generation and detection of high-frequency gravitational waves (HFGW). The advantages of electromagnetic systems are clearly seen in the proposed complete laboratory experiment, where one has to ensure the efficiency of, both, the process of generation and the process of detection of HFGW. Within the family of electromagnetic systems, one still has a great variety of possible geometrical configurations, classical and quantum states of the electromagnetic field, detection strategies, etc. According to evaluations performed 30 years ago, the gap between the HFGW laboratory signal and its level of detectability is at least 4 orders of magnitude. Hopefully, new technologies of today can remove this gap and can make the laboratory experiment feasible. The laboratory experiment is bound to be expensive, but one should remember that a part of the cost is likely to be reimbursed from the Nobel prize money ! Electromagnetic systems seem also appropriate for the detection of high-frequency end of the spectrum of relic gravitational waves. Although the current effort to observe the stochastic background of relic gravitational waves is focused on the opposite, very low-frequency, end of the spectrum, it would be extremely valuable for fundamental science to detect, or put sensible upper limits on, the high-frequency relic gravitational waves. I will briefly discuss the origin of relic gravitational waves, the expected level of their high-frequency signal, and the existing estimates of its detectability.
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