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In this paper, we study the polarization of a gravitational wave (GW) emitted by an astrophysical source at a cosmic distance propagating through the Friedmann-Lema^itre-Robertson-Walk universe. By considering the null geodesic deviations, we first provide a definition of the polarization of the GW in terms of the Weyl scalars with respect to a parallelly-transported frame along the null geodesics, and then show explicitly that, due to different effects of the expansion of the universe on the two polarization modes, the so-called + and $times$ modes, the polarization angle of the GW changes generically, when it is propagating through the curved background. By direct computations of the polarization angle, we show that different epochs, radiation-, matter- and $Lambda$-dominated, have different effects on the polarization. In particular, for a GW emitted by a binary system, we find explicitly the relation between the change of the polarization angle $|Delta varphi|$ and the redshift $z_s$ of the source in different epochs. In the $Lambda$CDM model, we find that the order of $|Delta varphi|{eta_0 F}$ is typically $O(10^{-3})$ to $O(10^3)$, depending on the values of $z_s$, where $eta_0$ is the (comoving) time of the current universe, and $FequivBig(frac{5}{256}frac{1}{tau_{obs}}Big)^{3/8}left(G_NM_cright)^{-5/8}$ with $tau_{obs}$ and $M_c$ being, respectively, the time to coalescence in the observers frame and the chirp mass of the binary system.
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We discuss the prospects of gravitational lensing of gravitational waves (GWs) coming from core-collapse supernovae (CCSN). As the CCSN GW signal can only be detected from within our own Galaxy and the local group by current and upcoming ground-based GW detectors, we focus on microlensing. We introduce a new technique based on analysis of the power spectrum and association of peaks of the power spectrum with the peaks of the amplification factor to identify lensed signals. We validate our method by applying it on the CCSN-like mock signals lensed by a point mass lens. We find that the lensed and unlensed signal can be differentiated using the association of peaks by more than one sigma for lens masses larger than 150 solar masses. We also study the correlation integral between the power spectra and corresponding amplification factor. This statistical approach is able to differentiate between unlensed and lensed signals for lenses as small as 15 solar masses. Further, we demonstrate that this method can be used to estimate the mass of a lens in case the signal is lensed. The power spectrum based analysis is general and can be applied to any broad band signal and is especially useful for incoherent signals.
Interferometric detectors will very soon give us an unprecedented view of the gravitational-wave sky, and in particular of the explosive and transient Universe. Now is the time to challenge our theoretical understanding of short-duration gravitational-wave signatures from cataclysmic events, their connection to more traditional electromagnetic and particle astrophysics, and the data analysis techniques that will make the observations a reality. This paper summarizes the state of the art, future science opportunities, and current challenges in understanding gravitational-wave transients.
It has been a half-decade since the first direct detection of gravitational waves, which signifies the coming of the era of the gravitational-wave astronomy and gravitational-wave cosmology. The increasing number of the detected gravitational-wave events has revealed the promising capability of constraining various aspects of cosmology, astronomy, and gravity. Due to the limited space in this review article, we will briefly summarize the recent progress over the past five years, but with a special focus on some of our own work for the Key Project Physics associated with the gravitational waves supported by the National Natural Science Foundation of China. In particular, (1) we have presented the mechanism of the gravitational-wave production during some physical processes of the early Universe, such as inflation, preheating and phase transition, and the cosmological implications of gravitational-wave measurements; (2) we have put constraints on the neutron star maximum mass according to GW170817 observations; (3) we have developed a numerical relativity algorithm based on the finite element method and a waveform model for the binary black hole coalescence along an eccentric orbit.
The observation of binary neutron star merger GW170817, along with its optical counterpart, provided the first constraint on the Hubble constant $H_0$ using gravitational wave standard sirens. When no counterpart is identified, a galaxy catalog can be used to provide the necessary redshift information. However, the true host might not be contained in a catalog which is not complete out to the limit of gravitational-wave detectability. These electromagnetic and gravitational-wave selection effects must be accounted for. We describe and implement a method to estimate $H_0$ using both the counterpart and the galaxy catalog standard siren methods. We perform a series of mock data analyses using binary neutron star mergers to confirm our ability to recover an unbiased estimate of $H_0$. Our simulations used a simplified universe with no redshift uncertainties or galaxy clustering, but with different magnitude-limited catalogs and assumed host galaxy properties, to test our treatment of both selection effects. We explore how the incompleteness of catalogs affects the final measurement of $H_0$, as well as the effect of weighting each galaxys likelihood of being a host by its luminosity. In our most realistic simulation, where the simulated catalog is about three times denser than the density of galaxies in the local universe, we find that a 4.4% measurement precision can be reached using galaxy catalogs with 50% completeness and $sim 250$ binary neutron star detections with sensitivity similar to that of Advanced LIGOs second observing run.
A passing gravitational wave causes a deflection in the apparent astrometric positions of distant stars. The effect of the speed of the gravitational wave on this astrometric shift is discussed. A stochastic background of gravitational waves would result in a pattern of astrometric deflections which are correlated on large angular scales. These correlations are quantified and investigated for backgrounds of gravitational waves with sub- and super-luminal group velocities. The statistical properties of the correlations are depicted in two equivalent and related ways: as correlation curves and as angular power spectra. Sub-(super-)luminal gravitational wave backgrounds have the effect of enhancing (suppressing) the power in low-order angular modes. Analytical representations of the redshift-redshift and redshift-astrometry correlations are also derived. The potential for using this effect for constraining the speed of gravity is discussed.
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