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Register a new userPolarization distortions of lensed gravitational waves
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In general relativity (GR), gravitational waves (GWs) propagate the well-known plus and cross polarization modes which are the signature of a massless spin-2 field. However, diffraction of GWs caused by intervening objects along the line of sight can cause the apparent rise of additional polarizations due to GW-curvature interactions. In this paper, we continue the analysis by two of the authors of the present article, on lensing of gravitational waves beyond geometric optics. In particular, we calculate the lensing effect caused by a point-like lens, in the regime where its Schwarzschild radius $R_s$ is much smaller than the wavelength $lambda$ of the signal, itself smaller than the impact parameter $b$. In this case, the curvature of spacetime induces distortions in the polarization of the wave such that effective scalar and vector polarizations may appear. We find that the amplitude of these apparent non-GR polarizations is suppressed by a factor $R_slambda/b^2$ with respect to the amplitude of the GR-like tensor modes. We estimate the probability to develop these extra polarization modes for a nearly monochromatic GW in the Pulsar Timing Arrays band traveling through a distribution of galaxies.
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Similar to light, gravitational waves (GWs) can be lensed. Such lensing phenomena can magnify the waves, create multiple images observable as repeated events, and superpose several waveforms together, inducing potentially discernible patterns on the waves. In particular, when the lens is small, $lesssim 10^5 M_odot$, it can produce lensed images with time delays shorter than the typical gravitational-wave signal length that conspire together to form ``beating patterns. We present a proof-of-principle study utilizing deep learning for identification of such a lensing signature. We bring the excellence of state-of-the-art deep learning models at recognizing foreground objects from background noises to identifying lensed GWs from noise present spectrograms. We assume the lens mass is around $10^3 M_odot$ -- $10^5 M_odot$, which can produce the order of millisecond time delays between two images of lensed GWs. We discuss the feasibility of distinguishing lensed GWs from unlensed ones and estimating physical and lensing parameters. Suggested method may be of interest to the study of more complicated lensing configurations for which we do not have accurate waveform templates.
Gravitational waves from the distant sources are gravitationally lensed during their propagation through the intervening matter inhomogeneities before arriving at detectors. It has been proposed in the literature that the variance of the lensed waveform can be used to extract information of the matter power spectrum at very small scales and of low-mass dark halos. In this paper, we show that the variance of the amplitude fluctuation and that of the phase fluctuation of the lensed waveform obey a simple relation irrespective of the shape of the matter power spectrum. We study conditions under which this relation can be violated and discuss some potential applications of the relation. This relation may be used to confirm the robustness of claimed observations of gravitational lensing of gravitational waves and the subsequent reconstruction of the matter power spectrum.
Cosmological Gravitational Waves (GWs) are usually associated with the transverse-traceless part of the metric perturbations in the context of the theory of cosmological perturbations. These modes are just the usual polarizations `+ and `x which appear in the general relativity theory. However, in the majority of the alternative theories of gravity, GWs can present more than these two polarization states. In this context, the Newman-Penrose formalism is particularly suitable for evaluating the number of non-null GW modes. In the present work we intend to take into account these extra polarization states for cosmological GWs in alternative theories of gravity. As an application, we derive the dynamical equations for cosmological GWs for two specific theories, namely, a general scalar-tensor theory which presents four polarization states and a massive bimetric theory which is in the most general case with six polarization states for GWs. The mathematical tool presented here is quite general, so it can be used to study cosmological perturbations in all metric theories of gravity.
Gravitational waves perturb the paths of photons, impacting both the time-of-flight and the arrival direction of light from stars. Pulsar timing arrays can detect gravitational waves by measuring the variations in the time of flight of radio pulses, while astrometry missions such as Gaia can detect gravitational waves from the time-varying changes in the apparent position of a field of stars. Just as gravitational waves impart a characteristic correlation pattern in the arrival times of pulses from pulsars at different sky locations, the deflection of starlight is similarly correlated across the sky. Here we compute the astrometric correlation patterns for the full range of polarization states found in alternative theories of gravity, and decompose the sky-averaged correlation patterns into vector spherical harmonics. We find that the tensor and vector polarization states produce equal power in the electric- and magnetic-type vector spherical harmonics, while the scalar modes produce only electric-type correlations. Any difference in the measured electric and magnetic-type correlations would represent a clear violation of Einstein gravity. The angular correlations functions for the vector and scalar longitudinal modes show the same enhanced response at small angular separations that is familiar from pulsar timing.
Vacuum gravitational fields invariant for a non Abelian Lie algebra generated by two Killing fields whose commutator is light-like are analyzed. It is shown that they represent nonlinear gravitational waves obeying to two nonlinear superposition laws. The energy and the polarization of this family of waves are explicitely evaluated.
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