Gravitational-wave (GW) observations by a network of ground-based laser interferometric detectors allow us to probe the nature of GW polarizations. This would be an interesting test of general relativity (GR), since GR predicts only two polarization modes while there are theories of gravity that predict up to six polarization modes. The ability of GW observations to probe the nature of polarizations is limited by the available number of linearly independent detectors in the network. (To extract all polarization modes, there should be at least as many detectors as the polarization modes.) Strong gravitational lensing of GWs offers a possibility to significantly increase the effective number of detectors in the network. Due to strong lensing (e.g., by galaxies), multiple copies of the same signal can be observed with time delays of several minutes to weeks. Owing to the rotation of the earth, observation of the multiple copies of the same GW signal would allow the network to measure different combinations of the same polarizations. This effectively multiplies the number of detectors in the network. Focusing on strongly lensed signals from binary black hole mergers that produce two observable "images", using Bayesian model selection and assuming simple polarization models, we show that our ability to distinguish between polarization models is significantly improved.
Alternative theories of gravity predict up to six distinct polarization modes for gravitational waves. Strong gravitational lensing of gravitational waves allows us to probe the polarization content of these signals by effectively increasing the number of observations from the same astrophysical source. The lensing time delays due to the multiple observed lensed images combined with the rotation of the Earth allows for effective non-collocated interferometers to be defined with respect to the source location and hence probe the alternative polarization amplitudes with more observations. To mea…
Current constraints on Einstein's weak equivalence principle (WEP) utilize the observed time delay between correlated particles of astronomical sources. However, the intrinsic time delay due to particle emission time is impossible to measure and is simply assumed to be zero in previous studies. Here we propose a robust method to test WEP for relativistic messengers using strongly lensed cosmic transients, which can naturally overcome the intrinsic time delay problem. This can be achieved in two ways: by comparing the time delays between lensed images seen in different energy bands or in gravit…
Testing Screened Modified Gravity with Strongly Lensed Gravitational Waves
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天体物理研究所）
The possible variation of the electromagnetic fine structure constant $α_e$ on cosmological scales arouses great interests in recent years. The strongly lensed gravitational waves and the electromagnetic counterparts could be used to test this variation. Under the assumption that the speed of photon could be modified, while the speed of GW is the same as GR predicated, and they both propagate in a flat Friedman-Robertson-Walker universe, we investigate the difference of time delays of the images and derive the upper bound of the variation of $α_e$. For a typical lensing system in the standard …
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 radi…
Probing the relative speeds of gravitational waves and light acts as an important test of General Relativity and alternative theories of gravity. Measuring the arrival time of gravitational waves and electromagnetic counterparts can be used to measure the relative speeds, but only if the intrinsic time-lag between emission of the photons and gravitational waves is well understood. Here we suggest a method that does not make such an assumption, using future strongly lensed GW events and EM counterparts; Biesiada et al forecast that 50-100 strongly lensed GW events will be observed each year wit…
Gravitational Faraday Rotation (GFR) is a frame-dragging effect induced by rotating massive objects, which is one of the important, yet studied characteristics of lensed gravitational waves (GWs). In this work, we calculate the GFR angle $χ_g$ of GWs in the weak deflection limit, assuming it is lensed by a Kerr black hole (BH). We find that the GFR effect changes the initial polarization state of the lensed GW. Compared with the Einstein deflection angle, the dominant term of the rotation angle $χ_g$ is a second-order correction to the polarization angle, which depends on the light-of-sight co…
Modified gravitational wave propagation is a smoking gun of modifications of gravity at cosmological scales, and can be the most promising observable for testing such theories. The observation of gravitational waves (GW) in recent years has allowed us to start probing this effect, and here we briefly review two promising ways of testing it. We will show that, already with the current network of detectors, it is possible to reach an interesting accuracy in the estimation of the $Ξ_0$ parameter (that characterizes modified gravitational wave propagation, with $Ξ_{0, {\rm GR}} = 1$) and with next…
The LIGO/Virgo gravitational wave events S190828j and S190828l were detected only 21 minutes apart, from nearby regions of sky, and with the same source classifications (binary black hole mergers). It is therefore natural to speculate that the two signals are actually strongly lensed images of the same merger. However, an estimate of the separation of the (unknown) positions of the two events requires them to be >10 deg apart, much wider than the arcsecond-scale separations that usually arise in extragalactic lensing. The large separation is much more consistent with two independent, unrelated…
We consider gravitational wave (GW) sources with an associated electromagnetic (EM) counterpart, and analyze the time delay between both signals in the presence of lensing. If GWs have wavelengths comparable to the Schwarzschild radius of astrophysical lenses, they must be treated with wave optics, whereas EM waves are typically well within the approximation of geometric optics. With concrete examples, we confirm that the GW signal never arrives before its EM counterpart, if both are emitted at the same time. However, during the inspiral of a binary, peaks of the GW waveform can arrive before …
We present a new idea of testing the validity of the Friedman-Lema\^ıtre-Robertson-Walker metric, through the multiple measurements of galactic-scale strong gravitational lensing systems with type Ia supernovae in the role of sources. Each individual lensing system will provide a model-independent measurement of the spatial curvature parameter referring only to geometrical optics independently of the matter content of the universe. This will create a valuable opportunity to test the FLRW metric directly. Our results show that with hundreds of strongly lensed SNe Ia observed by LSST, one would …
Violations of both the weak equivalence principle (WEP) and Lorentz invariance can produce vacuum birefringence, which leads to an energy-dependent rotation of the polarization vector of linearly polarized emission from a given astrophysical source. However, the search for the birefringent effect has been hindered by our ignorance concerning the intrinsic polarization angle in different energy bands. Considering the contributions to the observed linear polarization angle from both the intrinsic polarization angle and the rotation angles induced by violations of the WEP and Lorentz invariance, …
General relativity has predicted the existence of gravitational waves (GW), which are waves of the distortions of space-time with two degrees of polarization and the propagation speed of light. Alternative theories predict more polarizations, up to a maximum of six, and possible deviation of propagation speed from the light speed. The present paper reviews recent proposals to test the gravity theories in the radiation regime by observing GWs using pulsar timing arrays.
Testing Extra-Dimensional Gravitational-Wave Polarizations with Compact-Binary Observations
Dalian University of Technology（大连理工大学）；Southern Medical University（南方医科大学）；Peking University（北京大学）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；Lanzhou University（兰州大学）
The Einstein's equivalence principle can be tested by using parameterized post-Newtonian parameters, of which the parameter $γ$ has been constrained by comparing the arrival times of photons with different energies. It has been constrained by a variety of astronomical transient events, such as gamma-ray bursts (GRBs), fast radio bursts as well as pulses of pulsars, with the most stringent constraint of $Δγ\lesssim 10^{-15}$. In this letter, we consider the arrival times of lights with different circular polarization. For a linearly polarized light, it is the combination of two circularly polar…
While general relativity predicts only two tensor modes for gravitational wave polarization, general metric theories of gravity allows up to four additional modes, including two vector and two scalar modes. Observing the polarization modes of gravitational waves could provide a direct test of the modified gravity. The stochastic gravitational wave background (SGWB), which may be detected by space-based laser-interferometric detectors at design sensitivity, will provide an opportunity to directly measure alternative polarization. In this paper, we investigate the performance of the LISA-TianQin…
We apply the analogy between gravitational fields and optical media in the general relativistic geometric optics framework to describe how light can acquire orbital angular momentum (OAM) when it traverses the gravitational field of a massive rotating compact object and the interplay between OAM and polarization. Kerr spacetimes are known not only to impose a gravitational Faraday rotation on the polarization of a light beam, but also to set a characteristic fingerprint in the orbital angular momentum distribution of the radiation passing nearby a rotating black hole (BH). Kerr spacetime behav…
Discovery of strongly-lensed gravitational wave (GW) sources will unveil binary compact objects at higher redshifts and lower intrinsic luminosities than is possible without lensing. Such systems will yield unprecedented constraints on the mass distribution in galaxy clusters, measurements of the polarization of GWs, tests of General Relativity, and constraints on the Hubble parameter. Excited by these prospects, and intrigued by the presence of so-called "heavy black holes" in the early detections by LIGO-Virgo, we commenced a search for strongly-lensed GWs and possible electromagnetic counte…
The canonical acoustic dark energy model (cADE), which is based on a scalar field with a canonical kinetic term that rapidly converts potential to kinetic energy around matter radiation equality, alleviates the Hubble tension found in $Λ$CDM. We show that it successfully passes new consistency tests in the CMB damping tail provided by the ACT data, while being increasingly constrained and distinguished from alternate mechanisms by the improved CMB acoustic polarization data from Planck. The best fit cADE model to a suite of cosmological observations, including the SH0ES $H_0$ measurement, has …
We devise a test of nonlinear departures from general relativity (GR) using time delays in strong gravitational lenses. We use a phenomenological model of gravitational screening as a step discontinuity in the measure of curvature per unit mass, at a radius $Λ$. The resulting slip between two scalar gravitational potentials leads to a shift in the apparent positions and time delays of lensed sources, relative to the GR predictions, of size $γ_{\rm PN}-1$. As a proof of principle, we use measurements of two lenses, RXJ1121-1231 and B1608+656, to constrain deviations from GR to be below $|γ_{\rm…
The B-mode polarization in the cosmic microwave background (CMB) anisotropies at large angular scales provides a smoking-gun evidence for the primordial gravitational waves (GWs). It is often stated that a discovery of the GWs establishes the quantum fluctuation of vacuum during the cosmic inflation. Since the GWs could also be generated by source fields, however, we need to check if a sizable signal exists due to such source fields before reaching a firm conclusion when the B-mode is discovered. Source fields of particular types can generate non-Gaussianity (NG) in the GWs. Testing statistics…
Testing gravitational wave polarizations with LISA
Jagiellonian University（雅盖隆大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；CEICO, FZU – Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；University of Pennsylvania（宾夕法尼亚大学）；Universidad Andrés Bello（安德烈斯·贝略大学）；Université de Toulouse（图卢兹大学）；Swansea University（斯旺西大学）；Università di Bologna（博洛尼亚大学）；Niels Bohr Institute（尼尔斯·玻尔研究所）
The formation of the microwave background polarization anisotropies is investigated when the stochastic Faraday rate is stationary, random and Markovian. The scaling properties of the polarization power spectra and of their nonlinear combinations are scrutinized as a function of the comoving frequency. It is argued that each frequency channel of a given experiment measuring simultaneously the E-mode and the B-mode spectra can be analyzed in this framework with the aim of testing the physical origin of the polarization in a model-independent perspective.
