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We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.

In the data obtained by laser interferometric gravitational wave detectors, transient noise with non-stationary and non-Gaussian features occurs at a high rate. This often results in problems such as detector instability and the hiding and/or imitation of gravitational-wave signals. This transient noise has various characteristics in the time–frequency representation, which is considered to be associated with environmental and instrumental origins. Classification of transient noise can offer clues for exploring its origin and improving the performance of the detector. One approach for accomplishing this is supervised learning. However, in general, supervised learning requires annotation of the training data, and there are issues with ensuring objectivity in the classification and its corresponding new classes. By contrast, unsupervised learning can reduce the annotation work for the training data and ensure objectivity in the classification and its corresponding new classes. In this study, we propose an unsupervised learning architecture for the classification of transient noise that combines a variational autoencoder and invariant information clustering. To evaluate the effectiveness of the proposed architecture, we used the dataset (time–frequency two-dimensional spectrogram images and labels) of the Laser Interferometer Gravitational-wave Observatory (LIGO) first observation run prepared by the Gravity Spy project. The classes provided by our proposed unsupervised learning architecture were consistent with the labels annotated by the Gravity Spy project, which manifests the potential for the existence of unrevealed classes.

We introduce a new analysis method to deal with stationary non-Gaussian noises in gravitational wave detectors in terms of the independent component analysis. First, we consider the simplest case where the detector outputs are linear combinations of the inputs, consisting of signals and various noises, and show that this method may be helpful to increase the signal-to-noise ratio. Next, we take into account the time delay between the inputs and the outputs. Finally, we extend our method to nonlinearly correlated noises and show that our method can identify the coupling coefficients and remove non-Gaussian noises. Although we focus on gravitational wave data analysis, our methods are applicable to the detection of any signals under non-Gaussian noises.

Abstract The Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is a future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could have been produced during the inflationary period right after the birth of the Universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the Universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry–Pérot Michelson interferometers with an arm length of 1000 km. Three DECIGO clusters will be placed far from each other, and the fourth will be placed in the same position as one of the other three to obtain correlation signals for the detection of primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder for DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand multi-messenger astronomy.

Pre-DECIGO (DECihertz laser Interferometer Gravitational wave Observatory) consists of three spacecraft arranged in an equilateral triangle with 100 km arm lengths orbiting 2000 km above the surface of the earth. It is hoped that the launch date will be in the late 2020s.Pre-DECIGO has one clear target: binary black holes (BBHs) like GW150914 and GW151226. Pre-DECIGO can detect ~30M⊙–30M⊙ BBH mergers like GW150914 up to redshift z~30. The cumulative event rate is ~1.8×105 events yr−1 in the Pop III origin model of BBHs like GW150914, and it saturates at z~10, while in the primordial BBH (PBBH) model, the cumulative event rate is ~3×104 events yr−1 at z=30 even if only 0.1% of the dark matter consists of PBHs, and it is still increasing at z=30. In the Pop I/II model of GW150914-like BBHs, the cumulative event rate is (3–10) × 105 events yr−1 and it saturates at z~6. We present the requirements on orbit accuracy, drag-free techniques, laser power, frequency stability, and interferometer test mass. For BBHs like GW150914 at 1 Gpc (z~0.2), SNR~90 is achieved with the definition of Pre-DECIGO in the 0.01–100 Hz band. Since for z≫1 the characteristic strain amplitude hc for a fixed frequency band weakly depends on z as z−1/6, ∼ 10% of BBHs near face-on have SNR > 5 (7) even at z~30 (10). Pre-DECIGO can measure the mass spectrum and the z-dependence of the merger rate to distinguish various models of BBHs like GW150914, such as Pop III BBH, Pop II BBH, and PBBH scenarios.Pre-DECIGO can also predict the direction of BBHs at z=0.1 with an accuracy of ~0.3 deg2 and a merging time accuracy of ~1 s at about a day before the merger so that ground-based GW detectors further developed at that time as well as electromagnetic follow-up observations can prepare for the detection of merger in advance, like a solar eclipse. For intermediate mass BBHs such as ~640M⊙–640M⊙ at a large redshift z>10, the quasinormal mode frequency after the merger can be within the Pre-DECIGO band so that the ringing tail can also be detectable to confirm the Einstein theory of general relativity with SNR~35.

DECIGO (DECi-hertz Interferometer Gravitational wave Observatory) is the planned Japanese space gravitational wave antenna, aiming to detect gravitational waves from astrophysically and cosmologically significant sources mainly between 0.1 Hz and 10 Hz and thus to open a new window for gravitational wave astronomy and for the universe. DECIGO will consists of three drag-free spacecraft arranged in an equilateral triangle with 1000 km arm lengths whose relative displacements are measured by a differential Fabry-Perot interferometer, and four units of triangular Fabry-Perot interferometers are arranged on heliocentric orbit around the sun. DECIGO is vary ambitious mission, we plan to launch DECIGO in era of 2030s after precursor satellite mission, B-DECIGO. B-DECIGO is essentially smaller version of DECIGO: B-DECIGO consists of three spacecraft arranged in an triangle with 100 km arm lengths orbiting 2000 km above the surface of the earth. It is hoped that the launch date will be late 2020s for the present..

WIMPs are promising dark matter candidates. When WIMPs collide with a mirror equipped with interferometric gravitational wave detectors, we expect that characteristic motions of the pendulum and mirror are excited, and those signals could be extracted by highly sophisticated sensors developed for gravitational wave detection. We analyze the motions of the pendulum and mirror, and estimate the detectability of these motions. For the \"Thin-ET\" detector, the signal to noise ratio may be 1.7(mDM100GeV), where mDM is the mass of a WIMP. We may set a more strict upper limit on the cross section between a WIMP and a nucleon than the limits obtained by other experiments so far when mDM is approximately lower than 0.2 GeV. We find an order of magnitude improvement in the upper limit around mDM = 0.2 GeV.

A rapidly spinning neutron star (NS) would emit a continuous gravitational wave (GW) detectable by the advanced LIGO, advanced Virgo, KAGRA and proposed third generation detectors such as the Einstein Telescope (ET). Such a GW does not propagate freely, but is affected by the Coulomb-type gravitational field of the NS itself. This effect appears as a phase shift in the GW depending on the NS mass. We have shown that mass of an isolated NS can, in principle, be determined if we could detect the continuous GW with two or more frequency modes. Indeed, our Monte Carlo simulations have demonstrated that mass of a NS with its ellipticity 10-6 at 1 kpc is typically measurable with precision of 20% using the ET, if the NS is precessing or has a pinned superfluid core and emits GWs with once and twice the spin frequencies. After briefly explaining our idea and results, this paper concerns with the effect of misalignment angle (\"wobble angle\" in the case of a precessing NS) on the mass measurement precision.