Polarization Of Gravitational Waves Research Articles

Polarization test of gravitational waves from compact binary coalescences

Gravitational waves have only two polarization modes in general relativity. However, there are six possible modes of polarization in a generic metric theory of gravity. Thus, tests of gravitational-wave polarization can be tools for pursuing the nature of space-time structure. The observations of gravitational waves with a worldwide network of interferometric detectors such as Advanced LIGO, Advanced Virgo, and KAGRA will make it possible to obtain the information of gravitational-wave polarization from detector signals. We study the separability of the polarization modes for the inspiral gravitational waves from the compact binary coalescences systematically. Unlike some other waveforms such as burst, the binary parameters need to be properly considered. We show that three polarization modes of gravitational waves would be separable with the global network of three detectors to some extent, depending on the signal-to-noise ratio and the duration of the signal. We also show that with four detectors the three polarization modes would be more easily distinguished by breaking a degeneracy of the polarization modes and even the four polarization modes would be separable.

Astrometric effects of gravitational wave backgrounds with non-Einsteinian polarizations

The Gaia mission offers a new opportunity to search for the low-frequency gravitational wave background using astrometric measurements. In this paper, the astrometric effect of gravitational waves is reviewed, with a particular focus on the effect of non-Einsteinian gravitational wave polarizations. A stochastic gravitational wave background generates a correlated vector field of astrometric deflections on the sky. A convenient decomposition for the correlation matrix is introduced, enabling it to be calculated for all possible gravitational wave polarizations and compared to the redshift correlations from the pulsar-timing literature; in the case of a general relativity background of transverse traceless gravitational waves, this also allows us to identify an astrometric analog of the famous Hellings-Downs curve. Finally, the cross correlation between the redshift and astrometric signal is also calculated; this may form the basis for future joint pulsar-timing and astrometry searches for arbitrarily polarized gravitational wave backgrounds.

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background.

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω_{0}^{T}<5.58×10^{-8}, Ω_{0}^{V}<6.35×10^{-8}, and Ω_{0}^{S}<1.08×10^{-7} at a reference frequency f_{0}=25 Hz.

Constraining Alternative Theories of Gravity Using Pulsar Timing Arrays.

The opening of the gravitational wave window by ground-based laser interferometers has made possible many new tests of gravity, including the first constraints on polarization. It is hoped that, within the next decade, pulsar timing will extend the window by making the first detections in the nanohertz frequency regime. Pulsar timing offers several advantages over ground-based interferometers for constraining the polarization of gravitational waves due to the many projections of the polarization pattern provided by the different lines of sight to the pulsars, and the enhanced response to longitudinal polarizations. Here, we show that existing results from pulsar timing arrays can be used to place stringent limits on the energy density of longitudinal stochastic gravitational waves. However, unambiguously distinguishing these modes from noise will be very difficult due to the large variances in the pulsar-pulsar correlation patterns. Existing upper limits on the power spectrum of pulsar timing residuals imply that the amplitude of vector longitudinal (VL) and scalar longitudinal (SL) modes at frequencies of 1/year are constrained, A_{VL}<4×10^{-16} and A_{SL}<4×10^{-17}, while the bounds on the energy density for a scale invariant cosmological background are Ω_{VL}h^{2}<4×10^{-11} and Ω_{SL}h^{2}<3×10^{-13}.

Polarizations of gravitational waves in Horndeski theory

We analyze the polarization content of gravitational waves in Horndeski theory. Besides the familiar plus and cross polarizations in Einstein’s General Relativity, there is one more polarization state which is the mixture of the transverse breathing and longitudinal polarizations. The additional mode is excited by the massive scalar field. In the massless limit, the longitudinal polarization disappears, while the breathing one persists. The upper bound on the graviton mass severely constrains the amplitude of the longitudinal polarization, which makes its detection highly unlikely by the ground-based or space-borne interferometers in the near future. However, pulsar timing arrays might be able to detect the polarization excited by the massive scalar field. Since additional polarization states appear in alternative theories of gravity, the measurement of the polarizations of gravitational waves can be used to probe the nature of gravity. In addition to the plus and cross states, the detection of the breathing polarization means that gravitation is mediated by massless spin 2 and spin 0 fields, and the detection of both the breathing and longitudinal states means that gravitation is propagated by the massless spin 2 and massive spin 0 fields.

Localization of transient gravitational wave sources: beyond triangulation

Rapid, accurate localization of gravitational wave transient events has proved critical to successful electromagnetic followup. In previous papers we have shown that localization estimates can be obtained through triangulation based on timing information at the detector sites. In practice, detailed parameter estimation routines use additional information and provide better localization than is possible based on timing information alone. In this paper, we extend the timing based localization approximation to incorporate consistency of observed signals with two gravitational wave polarizations, and an astrophysically motivated distribution of sources. Both of these provide significant improvements to source localization, allowing many sources to be restricted to a single sky region, with an area 40% smaller than predicted by timing information alone. Furthermore, we show that the vast majority of sources will be reconstructed to be circularly polarized or, equivalently, indistinguishable from face-on.

Circular polarization of gravitational waves from non-rotating supernova cores: a new probe into the pre-explosion hydrodynamics

Abstract We present an analysis of the circular polarization of gravitational waves (GWs) using results from three-dimensional (3D), general relativistic (GR) core-collapse simulations of a non-rotating 15 M⊙ star. For the signal detection, we perform a coherent network analysis taking into account the four interferometers of LIGO Hanford, LIGO Livingston, VIRGO, and KAGRA. We focus on the Stokes V parameter, which directly characterizes the asymmetry of the GW circular polarization. We find that the amplitude of the GW polarization becomes bigger for our 3D-GR model that exhibits strong activity of the standing accretion shock instability (SASI). Our results suggest that the SASI-induced accretion flows to the proto-neutron star (PNS) lead to a characteristic, low-frequency modulation (100–200 Hz) in both the waveform and the GW circular polarization. By estimating the signal-to-noise ratio of the GW polarization, we demonstrate that the detection horizon of the circular polarization extends by more than a factor of several times farther comparing to that of the GW amplitude. Our results suggest that the GW circular polarization, if detected, could provide a new probe into the pre-explosion hydrodynamics such as the SASI activity and the g-mode oscillation of the PNS.

The polarizations of gravitational waves

The direct detection of gravitational waves opens a new window to probe the nature of gravity, and it brings us into the era of multi-messenger astronomy.Gravitational wave has no effect on the geodesics of a test particle, but it affects the relative motion between two nearby test particles.To measure gravitational wave and its polarizations, we need to study the geodesic deviation equation for two nearby test particles.Since only the electric part of the Riemann tensor $R_{i0j0}$ appears in the geodesic deviation equation and it has six independent components,there are up to six possible polarization states in general metric theories of gravity.In terms of the electric part of the Riemann tensor, the six polarizations are defined as follows.$\\hat{P}_+=-R_{x0x0}+R_{y0y0}$ corresponds to the “+ mode, $\\hat{P}_\\times=2R_{x0y0}$ denotes the “$\\times$ mode,$\\hat{P}_b=R_{x0x0}+R_{y0y0}$ corresponds to the breathing mode, $\\hat{P}_x=R_{x0z0}$ corresponds to the vector-$x$ mode,$\\hat{P}_x=R_{y0z0}$ represents to the vector-$y$ mode, and $\\hat{P}_l=R_{z0z0}$ denotes the longitudinal mode.For weak, plane and null gravitational waves, these six polarizations can be classified based on their properties under the Lorentz transformation.In Einsteins general relativity, the gravitational waves are tensor waves and there are “+ and “$\\times$ modes of polarization.In Brans-Dicke theory, in addition to the “+ and “$\\times$ polarization states, the scalar breathing mode also appears, and all these threepolarizations are transverse modes. In the most general scalar-tensor theory of gravity, the Horndeski theory,the massive scalar field excites both the breathing and the longitudinal modes, so in addition to the “+ and “$\\times$ polarizations,there exists a single mix state consisting of both the breathing and the longitudinal modes. In the massless limit,the longitudinal mode disappears andthe mix state becomes the pure transverse breathing polarization as that in Brans-Dicke theory. The nonlinear $f$($R$) theory of gravitycan be written as a scalar-tensor theory of gravity, so the polarization states in $f$($R$) gravity are the sameas those in Horndeski theory except that there is no massless limit in $f$($R$) gravity.In Einstein-Aether theory, due to the existence of the unit timelike vector field,the local Lorentz invariance is violated. The gravitational waves propagate with speeds different from the speed of light,and there are five independent polarization states,the “+ state $\\hat{P}_+$, the “$\\times$ state $\\hat{P}_\\times$, the vector$-x$ state $\\hat{P}_x$, the vector$-y$ state $\\hat{P}_y$ and themix state consisting of both the breathing and the longitudinal modes excited by the scalar field.In TeVeS theory, the local Lorentz invariance is also broken,so the gravitational waves in TeVeS theory propagate with speeds different from the speed of light.There are six polarization states in TeVeS theory,$\\hat{P}_+$, $\\hat{P}_\\times$, $\\hat{P}_x$, $\\hat{P}_y$ and twomix states excited by the two scalar fields. Each of the mix states consists of both the breathing and the longitudinal modes.Because gravitational waves have different polarization states for different theories of gravity, the measurementof polarizations is a powerful tool in probing the nature of gravity.

Quantum mechanical systems interacting with different polarizations of gravitational waves in noncommutative phase space

Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase-space, a credible possibility of their detection lies in the present day gravitational wave detector set-ups, which effectively detects the relative length-scale variations ${\cal{O}}\left[10^{-23} \right]$. With this motivation, we have considered how a free particle and harmonic oscillator in a quantum domain will respond to linearly and circularly polarized gravitational waves if the given phase-space has a noncommutative structure. The results show resonance behaviour in the responses of both free particle and HO systems to GW with both kind of polarizations. We critically analyze all the responses, and their implications in possible detection of noncommutativity. We use the currently available upper-bound estimates on various noncommutative parameters to anticipate the relative size of various response terms. We also argue how the quantum harmonic oscillator system we considered here can be very relevant in context of the resonant bar detectors of GW which are already operational currently.

Gravitational Wave Polarizations in f (R) Gravity and Scalar-Tensor Theory

The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in f (R) gravity and Horndeski theory, both containing scalar modes. These theories predict that in addition to the familiar + and × polarizations, there are transverse breathing and longitudinal polarizations excited by the massive scalar mode and the new polarization is a single mixed state. It would be very difficult to detect the longitudinal polarization by interferometers, while pulsar timing array may be the better tool to detect the longitudinal polarization.

Exploring String Axions with Gravitational Waves

We explore the string axion dark matter with gravitational waves in Chern–Simons gravity. We show that the parametric resonance of gravitational waves occurs due to the axion coherent oscillation. Remarkably, the circular polarization of gravitational waves is induced by the parity violating Chern–Simons coupling. In fact, the gravitational waves should be enhanced ten times every 10 − 8 pc propagation in the presence of the axion dark matter with mass 10 − 10 eV provided the coupling constant l = 10 8 km . Hence, after 10 kpc propagation, the amplitude of gravitational waves is enhanced significantly and the polarization of gravitational waves becomes circular. However, we have never observed these signatures. This implies that the Chern–Simons coupling constant and/or the abundance of string axions should be constrained much stronger than the current limits.

Polarization-Based Tests of Gravity with the Stochastic Gravitational-Wave Background

The direct observation of gravitational waves with Advanced LIGO and Advanced Virgo offers novel opportunities to test general relativity in strong-field, highly dynamical regimes. One such opportunity is the measurement of gravitational-wave polarizations. While general relativity predicts only two tensor gravitational-wave polarizations, general metric theories of gravity allow for up to four additional vector and scalar modes. The detection of these alternative polarizations would represent a clear violation of general relativity. The LIGO-Virgo detection of the binary black hole merger GW170814 has recently offered the first direct constraints on the polarization of gravitational waves. The current generation of ground-based detectors, however, is limited in its ability to sensitively determine the polarization content of transient gravitational-wave signals. Observation of the stochastic gravitational-wave background, in contrast, offers a means of directly measuring generic gravitational-wave polarizations. The stochastic background, arising from the superposition of many individually unresolvable gravitational-wave signals, may be detectable by Advanced LIGO at design-sensitivity. In this paper, we present a Bayesian method with which to detect and characterize the polarization of the stochastic background. We explore prospects for estimating parameters of the background, and quantify the limits that Advanced LIGO can place on vector and scalar polarizations in the absence of a detection. Finally, we investigate how the introduction of new terrestrial detectors like Advanced Virgo aid in our ability to detect or constrain alternative polarizations in the stochastic background. We find that, although the addition of Advanced Virgo does not notably improve detection prospects, it may dramatically improve our ability to estimate the parameters of backgrounds of mixed polarization.

Polarization modes of gravitational wave for viable f ( R ) $f(R)$ models

In this paper, we study the gravitational wave polarization modes for some particular $f(R)$ models using Newman-Penrose formalism. We find two extra scalar modes of gravitational wave (longitudinal and transversal modes) in addition to two tensor modes of general relativity. We conclude that gravitational waves correspond to class $II_{6}$ under the Lorentz-invariant E(2) classification of plane null waves for these $f(R)$ models.

Data analysis of massive gravitational waves from gamma ray bursts

We investigate the detectability of massive mode of polarization of Gravitational Waves (GWs) in [Formula: see text] theory of gravity associated with Gamma Ray Bursts (GRBs) sources. We obtain the beam pattern function of Laser Interferometric Gravitational wave Observatory (LIGO) corresponding to the massive polarization of GWs and perform Bayesian analysis to study this polarization. It is found that the massive polarization component with a mass of [Formula: see text][Formula: see text]eV/c2 is too weak to be detected at LIGO with its current configuration.

GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence.

On August 14, 2017 at 10∶30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm rate of ≲1 in 27 000years. The signal was observed with a three-detector network matched-filter signal-to-noise ratio of 18. The inferred masses of the initial black holes are 30.5_{-3.0}^{+5.7}M_{⊙} and 25.3_{-4.2}^{+2.8}M_{⊙} (at the 90% credible level). The luminosity distance of the source is 540_{-210}^{+130} Mpc, corresponding to a redshift of z=0.11_{-0.04}^{+0.03}. A network of three detectors improves the sky localization of the source, reducing the area of the 90% credible region from 1160 deg^{2} using only the two LIGO detectors to 60 deg^{2} using all three detectors. For the first time, we can test the nature of gravitational-wave polarizations from the antenna response of the LIGO-Virgo network, thus enabling a new class of phenomenological tests of gravity.

LIGO and Virgo team up to spot black hole merger

The first detection by an observatory other than LIGO improves source localization and exposes the polarizations of gravitational waves. The first detection by an observatory other than LIGO improves source localization and exposes the polarizations of gravitational waves.

Probing dynamical gravity with the polarization of continuous gravitational waves

The direct detection of gravitational waves provides the opportunity to measure fundamental aspects of gravity which have never been directly probed before, including the polarization of gravitational waves. In the context of searches for continuous waves from known pulsars, we present novel methods to detect signals of any polarization content, measure the modes present and place upper limits on the amplitude of nontensorial components. This will allow us to obtain new model-independent, dynamical constraints on deviations from general relativity. We test this framework on multiple potential sources using simulated data from three advanced-era detectors at design sensitivity. We find that signals of any polarization will become detectable and distinguishable for characteristic strains $h\ensuremath{\gtrsim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}\sqrt{1\text{ }\text{ }\mathrm{yr}/T}$, for an observation time $T$. We also find that our ability to detect nontensorial components depends only on the power present in those modes, irrespective of the strength of the tensorial strain.

Minimal theory of quasidilaton massive gravity

We introduce a quasidilaton scalar field to the minimal theory of massive gravity with the Minkowski fiducial metric, in such a way that the quasidilaton global symmetry is maintained and that the theory admits a stable self-accelerating de Sitter solution. We start with a precursor theory that contains three propagating gravitational degrees of freedom without a quasidilaton scalar and introduce St\"uckelberg fields to covariantize its action. This makes it possible for us to formulate the quasidilaton global symmetry that mixes the St\"uckelberg fields and the quasidilaton scalar field. By the Hamiltonian analysis we confirm that the precursor theory with the quasidilaton scalar contains four degrees of freedom, three from the precursor massive gravity and one from the quasidilaton scalar. We further remove one propagating degree of freedom to construct the minimal quasidilaton theory with three propagating degrees of freedom, corresponding to two polarizations of gravitational waves from the minimal theory of massive gravity and one scalar from the quasidilaton field, by carefully introducing two additional constraints to the system in the Hamiltonian language. Switching to the Lagrangian language, we find self-accelerating de Sitter solutions in the minimal quasidilaton theory and analyze their stability. It is found that the self-accelerating de Sitter solution is stable in a wide range of parameters.

Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f(ϕ). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allow to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass MCS. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra ⟨ γ γ ζ ⟩ for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f(ϕ) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.

Extracting gravitational waves induced by plasma turbulence in the early Universe through an averaging process

This work is a follow-up to the paper, ‘Numerical relativity as a tool for studying the early Universe’. In this article, we determine if cosmological gravitational waves can be accurately extracted from a dynamical spacetime using an averaging process as opposed to conventional methods of gravitational wave extraction using a complex Weyl scalar. We calculate the normalized energy density, strain and degree of polarization of gravitational waves produced by a simulated turbulent plasma similar to what was believed to have existed shortly after the electroweak scale. This calculation is completed using two numerical codes, one which utilizes full general relativity calculations based on modified BSSN equations while the other utilizes a linearized approximation of general relativity. Our results show that the spectrum of gravitational waves calculated from the nonlinear code using an averaging process is nearly indistinguishable from those calculated from the linear code. This result validates the use of the averaging process for gravitational wave extraction of cosmological systems.