Polarization Of Gravitational Waves Research Articles

Constraining gravitational-wave polarizations with Taiji

Space-based gravitational-wave detectors consist of a triangle of three spacecraft, which makes it possible to detect polarization modes of gravitational waves due to the motion of the detectors in space. In this paper we explore the ability of Taiji to detect the polarization modes in the parametrized post-Einsteinian framework. Assuming massive black hole binaries with the total mass of $M=4\times10^5\,M_{\odot}$ at redshift of $z=1$, we find that Taiji can measure the dipole and quadruple emission ($\Delta\alpha_D/\alpha_D$ and $\Delta\alpha_Q/\alpha_Q$) with the accuracy of up to $\sim 0.04\%$, with the fiducial value of $\alpha_D=0.001$, the scalar transverse and longitudinal modes ($\Delta\alpha_B$ and $\Delta\alpha_L$) up to $\sim 0.01$, and the vector modes ($\Delta\alpha_V$) up to $\sim 0.0005$.

Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory

A generalized Brans-Dicke (GBD) theory in the framework of Palatini formalism is proposed in this paper. We derive the field equations by using the variational approach and obtain the linearized equations by using the weak-field approximation method. We show various properties of the geometrical scalar field in the Palatini-formalism of GBD theory: it is massless and source-free, which are different from the results given in the metric-formalism of GBD theory. Also, we investigate the polarization modes of gravitational waves (GWs) by using the geodesic deviation method and the Newman-Penrose method in the Palatini-GBD theory. It is observed that there are three polarizations modes and four oscillations in the Palatini-GBD theory. Concretely, they are the two transverse tensor (+) and (×) standard polarization modes, and one breathing mode (with two oscillations). The results of GWs polarization in the Palatini-GBD theory are different from that in the metric-GBD theory, where there are four polarizations modes: the two standard tensorial modes (+ and ×), a scalar breathing mode, and a massive scalar mode that is a mix of the longitudinal and the breathing polarization. Comparing with the Palatini-f(R˜) theory and the General Relativity, we can see that the extra breathing mode of GWs polarization can be found in the Palatini-GBD theory. At last, the expression of the parameterized post Newton (PPN) parameter is derived, which could pass through the experimental test.

Gravitational waves and geometrical optics in scalar-tensor theories

The detection of gravitational waves (GWs) propagating through cosmic structures can provide invaluable information on the geometry and content of our Universe as well as on the fundamental theory of gravity. In order to test possible departures from General Relativity, it is essential to analyze, in a modified gravity setting, how GWs propagate through a perturbed cosmological space-time. Working within the framework of geometrical optics, we develop tools to address this topic for a broad class of scalar-tensor theories, including scenarios with non-minimal, derivative couplings between scalar and tensor modes. By focussing on a set-up where scalar modes propagate with the same speed as tensor degrees of freedom, we determine the corresponding evolution equations for the GW amplitude and polarization tensor. The former satisfies a generalized evolution equation that includes possible effects due to a variation of the effective Planck scale; the latter can fail to be parallel transported along the GW geodesics unless certain conditions are satisfied. We apply our general formulas to specific scalar-tensor theories with unit tensor speed, and then focus on GW propagation on a perturbed space-time. We determine corrections to standard formulas for the GW luminosity distance and for the evolution of the polarization tensor, which depend both on modified gravity and on the effects of cosmological perturbations. Our results can constitute a starting point to disentangle among degeneracies from different sectors that can influence GW propagation through cosmological space-times.

Constraining Gravitational Wave Polarization with GW190521 and ZTF19abanrhr

Abstract Gravitational waves (GWs) in general relativity are assumed to contain only tensorial polarization states, with generic metric theories of gravity also allowing for vector- and scalar-polarized GWs. Assuming an association between the gravitational-wave and electromagnetic transients GW190521 and ZTF19abanrhr, we find a preference for tensorial GWs with a log10 Bayes factor of 21.6 (with respect to vector-polarized GWs) and 38.4 (with respect to scalar-polarized GWs).

Considerations on gravitational waves in higher-order local and non-local gravity

The detection of gravitational wave modes and polarizations could constitute an extremely important signature to discriminate among different theories of gravity. According to this statement, it is possible to prove that higher-order non-local gravity has formally the same gravitational spectrum of higher-order local gravity. In particular, we consider the cases of f(R,□R,□2R,⋯,□nR)=R+∑i=1nαiR□iR gravity, linear with respect to both R and □iR and f(R,□R)=R+α(□R)2 gravity, quadratic with respect to □R, where it is demonstrated the graviton amplitude changes if compared with General Relativity. We also obtain the gravitational spectrum of higher-order non-local gravity f(R,□−1R,□−2R,⋯,□−nR)=R+∑i=1nαiR□−iR. In this case, we have three state of polarization and n+3 oscillation modes. More in detail, it is possible to derive two transverse tensor (+) and (×) standard polarization modes of frequency ω1, massless and with 2-helicity; n+1 further scalar modes of frequency ω2,…,ωn+2, massive and with 0-helicity, each of which has the same mixed polarization, partly longitudinal and partly transverse.

Pulse redshift of pulsar timing array signals for all possible gravitational wave polarizations in modified general relativity

Pulsar timing arrays (PTA) have the promise to detect gravitational waves (GWs) from sources which are in a unique frequency range of ${10}^{\ensuremath{-}9}\ensuremath{-}{10}^{\ensuremath{-}6}\text{ }\text{ }\mathrm{Hz}$. This in turn also provides an opportunity to test the theory of general relativity in the low frequency regime. The central concept of the detection of GWs with PTA lies in measuring the time of arrival difference of the pulsar signal due to the passing of GWs; i.e., the pulses get redshifted. In this paper we provide a complete derivation of the redshift computation for all six possible polarizations of GWs which arise due to the modifications to general relativity. We discuss the smoothness of the redshift and related properties at the critical point, where the GW source lies directly behind the pulsar. From our mathematical discussion we conclude that the redshift has to be split differently into polarization part (pattern functions) and interference part, to avoid discontinuities and singularities in the pattern functions. This choice of pattern functions agrees with the formula one uses for interferometers with a single detector arm. Finally, we provide a general expression which can in principle be used for pulsars and GWs of any frequency without invoking the low frequency assumption and using said assumption we develop the expression up to first order in the strain and find correction terms to the canonical redshift formula.

Towards a polarization prediction for LISA via intensity interferometry

ABSTRACT Compact Galactic Binary Systems with orbital periods of a few hours are expected to be detected in gravitational waves (GW) by Laser Interferometer Space Antenna (LISA) or a similar mission. At present, these so-called verification binaries provide predictions for GW frequency and amplitude. A full polarization prediction would provide a new method to calibrate LISA and other GW observatories, but requires resolving the orientation of the binary on the sky, which is not currently possible. We suggest a method to determine the elusive binary orientation and hence predict the GW polarization, using km-scale optical intensity interferometry. The most promising candidate is CD–30° 11223, consisting of a hot helium subdwarf with mB = 12 and a much fainter white dwarf companion, in a nearly edge-on orbit with period 70.5 min. We estimate that the brighter star is tidally stretched by 6 per cent. Resolving the tidal stretching would provide the binary orientation. The resolution needed is far beyond any current instrument, but not beyond current technology. We consider scenarios where an array of telescopes with km-scale baselines and/or the Very Large Telescope (VLT) and Extremely Large Telescope (ELT) are equipped with recently developed kilopixel sub-ns single-photon counters and used for intensity interferometry. We estimate that a team-up of the VLT and ELT could measure the orientation to ±1° at 2σ confidence in 24 h of observation.

Model-independent test of the parity symmetry of gravity with gravitational waves

Gravitational wave (GW) data can be used to test the parity symmetry of gravity by investigating the difference between left-hand and right-hand circular polarization modes. In this article, we develop a method to decompose the circular polarizations of GWs produced during the inspiralling stage of compact binaries, with the help of stationary phase approximation. The foremost advantage is that this method is simple, clean, independent of GW waveform, and is applicable to the existing detector network. Applying it to the mock data, we test the parity symmetry of gravity by constraining the velocity birefringence of GWs. If a nearly edge-on binary neutron-stars with observed electromagnetic counterparts at 40 Mpc is detected by the second-generation detector network, one could derive the model-independent test on the parity symmetry in gravity: the lower limit of the energy scale of parity violation can be constrained within mathcal {O}(10^4mathrm{eV}).

Generic searches for alternative gravitational wave polarizations with networks of interferometric detectors

The detection of gravitational wave signals by Advanced LIGO and Advanced Virgo enables us to probe the polarization content of gravitational waves. In general relativity, only tensor modes are present, while in a variety of alternative theories one can also have vector or scalar modes. Recently test were performed which compared Bayesian evidences for the hypotheses that either purely tensor, purely vector, or purely scalar polarizations were present. Indeed, with only three detectors in a network and allowing for mixtures of tensor polarizations and alternative polarization states, it is not possible to identify precisely which nonstandard polarizations might be in the signal and by what amounts. However, we demonstrate that one can still infer whether, in addition to tensor polarizations, alternative polarizations are present in the first place, irrespective of the detailed polarization content. We develop two methods to do this for sources with electromagnetic counterparts, both based on the so-called null stream. Apart from being able to detect mixtures of tensor and alternative polarizations, these have the added advantage that no waveform models are needed, and signals from any kind of transient source with known sky position can be used. Both formalisms allow us to combine information from multiple sources so as to arrive at increasingly more stringent bounds. For now we apply these on the binary neutron star signal GW170817, showing consistency with the tensor-only hypothesis with p-values of 0.315 and 0.790 for the two methods.

Polarized Initial States of Primordial Gravitational Waves

Polarizations of primordial gravitational waves can be relevant when considering an inflationary universe in modified gravity or when matter fields survive during inflation. Such polarizations have been discussed in the Bunch–Davies vacuum. Instead of taking into account the dynamical generation of polarizations of gravitational waves, in this paper, we consider polarized initial states constructed from S U ( 2 ) coherent states. We then evaluate the power spectrums of the primordial gravitational waves in the states.

Gravitational waves from the quasicircular inspiral of compact binaries in Einstein-aether theory

We study gravitational waves emitted by a binary system of nonspinning bodies in a quasicircular inspiral within the framework of Einstein-aether theory. In particular, we compute explicitly and analytically the expressions for the time-domain and frequency-domain waveforms, gravitational wave polarizations, and response functions for both ground- and space-based detectors in the post-Newtonian approximation. We find that, when going beyond the leading order in the post-Newtonian approximation, the non-Einsteinian polarization modes contain terms that depend on both the first and the second harmonics of the orbital phase. We also calculate analytically the corresponding parametrized post-Einsteinian parameters, generalizing the existing framework to allow for different propagation speeds among the scalar, vector, and tensor modes, without assumptions about the magnitude of its coupling parameters, and meanwhile, allowing the binary system to have relative motions with respect to the aether field. Such results allow for the easy construction of Einstein-aether templates that could be used in Bayesian tests of general relativity in the future.

Predictions of Cosmic Microwave Background Foreground Dust Polarization Using Velocity Gradients

Abstract Observations of fluctuations in the cosmic microwave background provide information about primordial inhomogeneities in the universe. However, the B-mode polarization of the inflationary gravitational wave is contaminated by the Galactic foreground polarized radiation arising from dust aligned by interstellar magnetic fields. To trace magnetic fields, we use the Velocity Gradient Technique (VGT), which employs modern understanding of the nature of magnetohydrodynamic turbulent motions. In this paper, we combine the VGT with Principal Component Analysis (PCA) to improve the accuracy of magnetic field tracing. We apply the VGT–PCA to the high-resolution neutral hydrogen data from the GALFA-H i survey to predict the polarization of dust. We report that the predicted directions of dust polarization provide good correspondence with those reported by Planck 353 GHz, with the alignment measure between the two ≃0.79 ± 0.01. We show that our results statistically agree with the Planck polarization in terms of magnetic field tracing. We find that the variation of dust emission efficiency across the sky is small. Using our maps of predicted polarization, we calculate the ratio of the E- and B-modes, and show that BB/EE ≃ 0.53 ± 0.10, which is similar to the result from Planck polarization.

Gravitational wave polarization in exponential forms of f(R) gravity with coupling to matter

We investigate polarizations of gravitational waves in generalized theories of gravity whose action contains a nonminimal coupling (NMC) between an exponential function of [Formula: see text] gravity and the matter field. Specifically, we consider two classes of such models. In the first case, we assume an explicit NMC between the matter Lagrangian density and curvature while in the second case, we consider the exponential [Formula: see text] gravity coupled to the trace of the stress-energy tensor of a scalar field. Using the Newman–Penrose quantities, we show that these models can be considered as suitable choices in order to produce new polarization modes.

Strong gravity signatures in the polarization of gravitational waves

General Relativity is a hugely successful description of gravitation. However, both theory and observations suggest that General Relativity might have significant classical and quantum corrections in the Strong Gravity regime. Testing the strong field limit of gravity is one of the main objectives of the future gravitational wave detectors. One way to detect strong gravity is through the polarization of gravitational waves. For quasi-normal modes of black-holes in General Relativity, the two polarization states of gravitational waves have the same amplitude and frequency spectrum. Using the principle of energy conservation, we show that the polarizations differ for modified gravity theories. We obtain a diagnostic parameter for polarization mismatch that provides a unique way to distinguish General Relativity and modified gravity theories in gravitational wave detectors.

Detecting the beaming effect of gravitational waves

The models currently used in the detection of gravitational waves (GWs) either do not consider a relative motion between the center-of-mass of the source and the observer, or usually only consider its effect on the frequencies of GWs. However, it is known for light waves that a relative motion not only changes the frequencies but also the brightness of the source, the latter of which is called the `beaming effect'. Here we investigate such an effect for GWs and find that the observed amplitude of a GW signal, unlike the behavior of light, is not a monotonic function of the relative velocity and responds differently to the two GW polarizations. We attribute the difference to a rotation of the wave-vector, as well as a reorientation of the GW polarizations. We find that even for velocities as small as $0.25\%$ of the speed of light, ignoring the aforementioned beaming effect could induce a systematic error that is larger than the designated calibration accuracy of LIGO. This error could lead to an incorrect estimation of the distance and orbital inclination of a GW source, or result in a spurious signal that appears to be incompatible with general relativity.

Constraining extra gravitational wave polarizations with Advanced LIGO, Advanced Virgo, and KAGRA and upper bounds from GW170817

General metric theories of gravity in four-dimensional spacetimes can contain at most six polarization modes (two spin-0, two spin-1 and two spin-2) of gravitational waves (GWs). It has been recently shown that, with using four GW non-coaligned detectors, a direct test of the spin-1 modes can be done in principle separately from the spin-0 and spin-2 modes for a GW source in particular sky positions [Hagihara et al., Phys. Rev. D 98, 064035 (2018)]. They have found particular sky positions that satisfy a condition of killing completely the spin-0 modes in a so-called null stream which is a linear combination of the signal outputs to kill the spin-2 modes. The present paper expands the method to discuss a possibility that the spin-0 modes are not completely but effectively suppressed in the null streams to test the spin-1 modes separately from the other modes, especially with an expected network of Advanced LIGO, Advanced Virgo and KAGRA. We study also a possibility that the spin-1 modes are substantially suppressed in the null streams to test the spin-0 modes separately from the other modes, though the spin-1 modes for any sky position cannot be completely killed in the null streams. Moreover, we find that the coefficient of the spin-0 modes in the null stream is significantly small for the GW170817 event, so that an upper bound can be placed on the amplitude of the spin-1 modes as $< 6 \times 10^{-23}$.

Sensitivity functions for space-borne gravitational wave detectors

Time-delay interferometry is put forward to improve the signal-to-noise ratio of space-borne gravitational wave detectors by canceling the large laser phase noise with different combinations of measured data. Based on the Michelson data combination, the sensitivity function of the detector can be obtained by averaging the all-sky wave source positions. At present, there are two main methods to encode gravitational wave signal into detector. One is to adapt gravitational wave polarization angle depending on the arm orientation in the gravitational wave frame, and the other is to divide the gravitational wave signal into plus and cross polarizations in the detector frame. Although there are some attempts using the first method to provide the analytical expression of sensitivity function, only a semianalytical one could be obtained. Here, starting with the second method, we demonstrate the equivalence of both methods. First time to obtain the full analytical expression of sensitivity function, which provides a fast and accurate mean to evaluate and compare the performance of different space-borne detectors, such as LISA and TianQin.

Prospects for gravitational-wave polarization tests from compact binary mergers with future ground-based detectors

There exist six possible polarization modes of gravitational waves in a general metric theory of gravity, while two tensor polarization modes are allowed in general relativity. The properties and number of polarization modes depend on gravity theories. For transient signals, the number of the detectors needs to be basically equal to the number of the gravitational-wave polarization modes for separation of polarizations. However, a single detector having great sensitivity at lower frequency could be effectively regarded as a virtual detector network including a set of detectors along its trajectory due to a long gravitational-wave signal from a compact binary and the Earth's rotation. Thus, time-varying antenna pattern functions can help test the polarizations of gravitational waves. We study the effects of the Earth's rotation on the polarization test and show a possibility to test the nontensorial polarization modes from future observations of compact binary mergers with ground-based gravitational detectors such as Einstein telescope and Cosmic Explorer.

Polarization of gravitational waves in symmetric teleparallel theories of gravity and their modifications

Symmetric teleparallel gravity (STG) offers an interesting avenue to formulate a theory of gravitation that relies neither on curvature nor torsion but only on nonmetricity $Q$. Given the growing number of confirmed observations of gravitational waves (GWs) and their use to explore gravitational theories, in this work we investigate the GWs in various extensions of STG, focusing on their speed and polarization. We explore the plethora of theories that this new framework opens up, that is, as general relativity can be modified, so can the symmetric teleparallel equivalent of general relativity (STEGR). In this work, we investigate the fate of GWs in the generalized irreducible decomposition of STEGR, generalizations of the STEGR Lagrangian, $f(Q)$, a scalar field nonminimally coupled to the STEGR Lagrangian, and the general setup of $f(Q,B)$ theory where $B$ is the boundary term difference between the Ricci scalar and the STEGR Lagrangian. Coincidentally, $f(Q,B)$ forms a more general theory than $f(R)$ gravity since $Q$ embodies the second-order elements of the Ricci scalar while $B$ takes on its fourth-order boundary terms. Our work deals mainly with the resulting scalar-vector-tensor polarization modes of the plethora of STG theories, and how they effect their respective speeds of propagation.

General Assertions on the Gravitational Waves Polarization Modes from an f(R) Model of Gravity

Detailed analysis of an f( R) theory is emphasized in a Minkowski and non trivial background. It is shown that the polarization modes depend strongly on the metric or Palatini formalism, Einstein or Jordan frame, function f (R ), background gravitational field and the observer.