Polarization Modes Of Gravitational Waves Research Articles

Exploring waveforms with non-GR deviations for extreme mass-ratio inspirals

The fundamental process of detecting and examining the polarization modes of gravitational waves plays a pivotal role in enhancing our grasp on the precise mechanisms behind their generation. A thorough investigation is essential for delving deeper into the essence of gravitational waves and rigorously evaluating and validating the range of modified gravity theories. In this line of interest, a general description of black holes in theories beyond general relativity can serve a meaningful purpose where distinct deviation parameters can be mapped to solutions representing distinct theories. Employing a refined version of the deformed Kerr geometry, which is free from pathological behaviours such as unphysical divergences in the metric, we explore an extreme mass-ratio inspiral system, wherein a stellar-mass object perturbs a supermassive black hole. We compute the effects of deformation parameters on the rate of change of orbital energy and angular momentum, orbital evolution and phase dynamics with leading order post-Newtonian corrections. With the waveform analysis, we assess the plausibility of detecting deviations from general relativity through observations facilitated by the Laser Interferometer Space Antenna (LISA), simultaneously constraining the extent of these deviations. Therefore, this analysis provides an understanding while highlighting the essential role of observations in advancing gravitational phenomena beyond general relativity.

Polarization modes of gravitational waves in general Einstein-vector theory

Polarization modes of gravitational waves in general Einstein-vector theory

Polarization modes of gravitational waves in general modified gravity: General metric theory and general scalar-tensor theory

Polarization modes of gravitational waves in general modified gravity: General metric theory and general scalar-tensor theory

Polarization modes of gravitational waves in generalized Proca theory

Polarization modes of gravitational waves in generalized Proca theory

Scalar polarization window in gravitational-wave signals

Abstract Scalar polarization modes of gravitational waves, which are often introduced in the context of the viable extension of gravity, have been actively searched for. However, couplings of the scalar modes to matter are strongly constrained by fifth-force experiments. Thus, the amplitude of scalar polarization in the observed gravitational-wave signal must be significantly suppressed compared to that of the tensor modes. Here, we discuss the implications of the experiments in the solar system on the detectability of scalar modes in gravitational waves from compact binary coalescences, taking into account the whole processes from the generation to the observation of gravitational waves. We first claim that the energy carried by the scalar modes at the generation is, at most, that of the tensor modes from the observed phase evolution of the inspiral gravitational waves. Next, we formulate general gravitational-wave propagation and point out that the energy flux hardly changes through propagation as long as the background changes slowly compared to the wavelength of the propagating waves. Finally, we show that the possible magnitude of scalar polarization modes detected by ground-based gravitational-wave telescopes is already severely constrained by the existing gravity tests in the solar system.

Gravitational waveform and polarizationfrom binary black hole inspiral in dynamical Chern-Simons gravity: from generation to propagation

We calculate the gravitational waveform radiated from spinning black holes (BHs) binary in dynamical Chern-Simons (dCS) gravity. The equation of motion (EOM) of the spinning binary BHs is derived based on the modified Mathisson-Papapetrou-Dixon equation for the spin-aligned circular orbits. The leading-order effects induced by the dCS theory contain spin-spin interaction and monopole-quadrupole interaction, which influences both the EOM of the binary system and corresponding gravitational waveform at the second post-Newtonian (PN) order (i.e., 2PN order). After reporting the waveforms, we investigate the polarization modes of gravitational waves (GWs) in dCS theory. None of the extra modes appears in this theory up to the considered PN order. Moreover, since the time scale of the binary merger is much smaller than that of the cosmological expansion, the parity-violating effect of the dCS theory does not appear in the process of GW generation. However, during the process of GW propagation, amplitude birefringence, a typical parity-violating effect, makes plus and cross modes convert to each other, which modifies the gravitational waveform at 1.5PN order.

Polarization of Gravitational Waves in Modified Gravity

An investigation has been carried out on a reconfigured form of the Einstein-Hilbert action, denoted by f(R,Tϕ), where Tϕ represents the energy-momentum tensor trace of the scalar field under consideration. The study has focused on how the structural behavior of the scalar field changes based on the potential’s shape, which has led to the development of a new set of Friedmann equations. In the context of modified theories, researchers have extensively explored the range of gravitational wave polarization modes associated with relevant fields. In addition to the two transverse-traceless tensor modes that are typically observed in general relativity, two additional scalar modes have been identified: a massive longitudinal mode and a massless transverse mode, also known as the breathing mode.

Bayesian analysis of the stochastic gravitational-wave background with alternative polarizations for space-borne detectors

Future space gravitational-wave detectors will detect gravitational waves with high sensitivity in the mHz frequency band. One possible source is the stochastic gravitational-wave background (SGWB), possibly from astronomy and cosmology. Detecting SGWB could provide an opportunity to directly examine the polarization of gravitational waves. While general relativity predicts only two tensor modes for gravitational-wave polarization, general metric theories of gravity allow up to four additional modes, including two vector and two scalar modes. Observing other polarization modes of gravitational waves would directly indicate that general relativity needs to be modified. However, the application of polarization identification methods developed for ground-borne detectors to space-borne detectors will require improvement. In this paper, we design a new statistic for the characteristics of space-borne detectors and perform Bayesian analysis. We analyze the performance of the new statistics, including the signal-to-noise ratio, ability to identify SGWB, and parameter estimation. The results show that the Bayesian method with new statistics is good enough to meet the needs of space detectors to identify polarized SGWB. In particular, space-borne gravitational-wave detectors will have the ability to distinguish the scalar-breathing mode and the scalar-longitudinal mode with this Bayesian method, which ground-based detectors cannot.

Constraining the extra polarization modes of gravitational waves with double white dwarfs

The detection of gravitational wave (GW) has opened a new window to test the theory of gravity in the strong field regime. In general relativity (GR), GW can only possess two tensor polarization modes, which are known as the $+$ and $\times$ modes. However, vector and scalar modes can exist in some modified theories of gravity, and we can test the gravitational theories by probing these extra polarization modes. As a space-borne GW detector, TianQin will be launched in the 2030s, and it is expected to observe plenty of GW signals, including those from nearly ten-thousands double white dwarfs (DWDs) in our galaxy. This offers an excellent chance for testing the existence of extra polarization modes. In this article, we analyze the capability of detecting the extra polarization modes with DWDs. For the extra modes, we consider both the leading order dipole radiation and the subleading quadrupole radiation. We find that the capability of TianQin has very strong dependency on the source orientation. We also analyze all the verification binaries with determined position and frequency, and find that ZTF J1539 can give the best constraint on the extra polarization modes. We have also considered the case of TianQin twin constellation, and the joint observation with LISA.

Detection of gravitational wave mixed polarization with single space-based detectors

General Relativity predicts only two tensor polarization modes for gravitational waves while at most six possible polarization modes are allowed in the general metric theory of gravity. The number of polarization modes is determined by the specific modified theory of gravity. Therefore, the determination of polarization modes can be used to test gravitational theory. We introduce a concrete data analysis pipeline for a space-based detector such as LISA to detect the polarization modes of gravitational waves. This method can be used for monochromatic gravitational waves emitted from any compact binary system with a known sky position and frequency to detect mixtures of tensor and extra polarization modes. We use the source $\mathrm{J}0806.3+1527$ with one year of simulation data as an example to show that this approach is capable of probing pure and mixed polarizations without knowing the exact polarization modes. We also find that the ability of detection of extra polarization depends on the gravitational-wave source location and the amplitude of nontensorial components.

Linearized field equations and extra force in f(R,T(n)) extended gravity

We consider an extended theory of gravity with Lagrangian [Formula: see text], with [Formula: see text] being a [Formula: see text]th-order invariant made of contractions of the energy–momentum tensor. When [Formula: see text], this theory reduces to [Formula: see text] gravity, where [Formula: see text] accounts for the trace of the energy–momentum tensor. We study the gravitational wave polarization modes, from which it results that when the matter Lagrangian contains dynamical scalar fields minimally coupled to the geometry, further polarization modes arise with respect to General Relativity. Finally, we show that the motion for test particles is nongeodesic and we explicitly obtain the extra force.

Search for scalar-tensor mixed polarization modes of gravitational waves

An additional scalar degree of freedom for a gravitational wave is often predicted in theories of gravity beyond general relativity and can be used for a model-agnostic test of gravity. In this letter, we report the direct search for the scalar-tensor mixed polarization modes of gravitational waves from compact binaries in a strong regime of gravity by analyzing the data of GW170814 and GW170817, which are the merger events of binary black holes and binary neutron stars, respectively. Consequently, we obtain the constraints on the ratio of scalar-mode amplitude to tensor-mode amplitude: $\lesssim 0.20$ for GW170814 and $\lesssim 0.068$ for GW170817, which are the tightest constraints on the scalar amplitude in a strong regime of gravity before merger.

Polarization modes of gravitational waves in Palatini-Horndeski theory

In this paper, the polarization modes of gravitational waves in Horndeski gravity are studied under the Palatini formalism. After obtaining the linearized equation of perturbations in Minkowski background, we find that the polarization modes of gravitational waves depend on the selection of the theoretical parameters. The polarization modes can be divided into quite rich cases by parameters. In all cases of parameter selection, there are $+$ and $\times$ modes propagating at the speed of light but no vector modes. The only difference from general relativity is scalar modes, especially the scalar degrees of freedom can be 0, 1 or 2 in different cases. The appropriate parameter cases can be expected to be selected in the detection of gravitational wave polarization modes by Lisa, Taiji and TianQin in the future.

Sensitivity of third-generation interferometers to extra polarizations in the stochastic gravitational wave background

When modified theories of gravity are considered, at most six gravitational wave polarization modes are allowed and classified in tensor modes, the only ones predicted by General Relativity (GR), along with additional vector and scalar modes. Therefore, gravitational waves represent a powerful tool to test alternative theories of gravitation. In this paper, we forecast the sensitivity of third-generation ground-based interferometers, Einstein Telescope and Cosmic Explorer, to non-GR polarization modes focusing on the stochastic gravitational wave background. We consider the latest technical specifications of the two independent detectors and the full network in order to estimate both the optimal signal-to-noise ratio and the detectable energy density limits relative to all polarization modes in the stochastic background for several locations on Earth and orientations of the two observatories. By considering optimal detector configurations, we find that in 5 years of observation the detection limit for tensor and extra polarization modes could reach $h_0^2\Omega^{T,V,S}_{GW} \approx 10^{-12}-10^{-11}$, depending on the network configuration and the stochastic background (i.e., if only one among vector and scalar modes exists or both are present). This means that the network sensitivity to different polarization modes can be approximately improved by a factor $10^3$ with respect to second-generation interferometers. We finally discuss the possibility of breaking the scalar modes degeneracy by considering both detectors angular responses to sufficiently high gravitational wave frequencies.

Quasinormal modes of black holes with non-linear-electrodynamic sources in Rastall gravity

One of the notable modifications of General Relativity (GR) is the Rastall gravity. We have studied the polarization modes of Gravitational Waves (GWs) in this gravity. It is found that at a very far distance away from the source of GWs, Rastall gravity behaves identically to GR. That is, we get only two massless tensor polarization modes of GWs in the theory. Afterwards, we have extended our study to quasinormal modes of black holes in Rastall gravity in presence of non-linear electrodynamic sources. Here the impacts of cosmological field, dust field, phantom field, quintessence field and radiation field on the quasinormal modes in presence of electrodynamic sources have been investigated. Apart from this, we have also checked the dependency of quasinormal modes with the Rastall parameter $\lambda$, black hole structural constant $N_s$ and charge of the black hole $Q$. The study shows that the quasinormal modes corresponding to the black hole with non-linear electrodynamic sources show significant deviations from a general charged black hole in Rastall gravity under certain conditions. Further, the behaviour of black holes and hence the quasinormal modes depend on the type of surrounding field considered.

Gravitational waves in $$\mathbf {f(R)}$$ gravity power law model

We investigate the different polarization modes of Gravitational Waves (GWs) in $f(R)$ gravity power law model in de Sitter space. It is seen that the massive scalar field polarization mode exists in this model. The mass of the scalar field depends highly on the background curvature and the power term $n$. However, we found that the model doesnot exhibit a massive scalar mode for $n=2$ and instead it shows a breathing mode in addition to the tensor plus and cross modes. Thus mass of the scalar field is found to vary with $n$ within the range $1 \leq n \leq 2$.

Complete set of GW polarization modes in higher-derivative $$f(R,\square R,T)$$ theories of gravity

In this paper, we investigate the gravitational waves in a particular class of alternative theories of gravity which is known as higher-derivative $f(R,\square R,T)$ gravity theory. In low curvature regime and by using Newman–Penrose analysis for the linear order of the field equations, we show that in addition to the usual plus and cross polarization modes which appear in general relativity, all other modes can exist too. Actually, according to our analysis, in such a theory by choosing the proper values from the parameter space of the model, a complete set of gravitational wave polarization modes can be produced in this concept.

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.

Searching for anomalous polarization modes of the stochastic gravitational wave background with LISA and Taiji

The vector and scalar polarization modes of gravitational waves do not exist in General Relativity, and their detection would have significant impacts on fundamental physics. In this paper, we explored the detectability of these anomalous polarization modes in a gravitational wave background around 1 mHz with the future LISA-Taiji network. The inherent geometrical symmetry of the network largely simplifies the correlation analysis. By taking a suitable linear combination of the correlated outputs, the contribution of the standard tensor modes can be canceled algebraically, and the anomalous modes can be exclusively examined. We provide concise expressions for the signal-to-noise ratios of the anomalous modes with this cancellation method. We also discuss the possibility of separately estimating the amplitudes of the vector and scalar modes, using the overall frequency dependence of the associated overlap reduction functions.