Polarization Of Gravitational Waves Research Articles

Measuring the circular polarization of gravitational waves with pulsar timing arrays

Measuring the circular polarization of gravitational waves with pulsar timing arrays

Probing massive gravitons in f(R) with lensed gravitational waves

We investigate the novel features of gravitational wave solutions in f(R) gravity under proper gauge considerations in the shifted Ricci scalar background curvature (R1+ϵ). The solution is further explored to study the modified dispersion relations for massive modes at local scales and to derive constraints on ϵ. Our analysis yields new insights as we scrutinize these dispersion effects on the polarization (modified Newman-Penrose content) and lensing properties of gravitational waves. It is discovered that the existing longitudinal scalar mode, and transverse breathing scalar mode are both independent of the mass parameter for ϵ<<1. Further, by analysing the lensing amplification factor for the point mass lens model, we show that lensing of gravitational wave is highly sensitive to these dispersion effects in the milli-Hertz frequency (wave optics regime). It is expected that ultra-light modes, having mass about O(10−15) eV for ϵ<<1(≈10−7) lensed by (103≤MLens≤106)M⊙ compact objects are likely to be detected by the advanced gravitational wave space-borne detectors, particularly within LISA's (The Laser Interferometer Space Antenna) sensitivity band.

Prospects of constraining on the polarizations of gravitational waves from binary black holes using space- and ground-based detectors

Prospects of constraining on the polarizations of gravitational waves from binary black holes using space- and ground-based detectors

Unveiling the existence of nontensorial gravitational-wave polarizations from individual supermassive black hole binaries with pulsar timing arrays

Unveiling the existence of nontensorial gravitational-wave polarizations from individual supermassive black hole binaries with pulsar timing arrays

Power spectra and circular polarization of primordial gravitational waves with parity and Lorentz violations

The violations of parity and Lorentz symmetries in gravity can change the propagating properties of gravitational waves (GWs) in the cosmological background, which can arise from a large number of parity- and Lorentz-violating theories. In this paper, through a systematic parametrization for characterizing possible derivations from the standard GW propagation in general relativity, we study both the parity- and Lorentz-violating effects on the power spectra and the polarization of the primordial gravitational waves (PGWs) during the slow-roll inflation. To this end, we calculate explicitly the power spectrum and the corresponding circular polarization of the PGWs analytically by using the uniform asymptotic approximation. It is shown that the new contributions to power spectra contain two parts, one from the parity-violating terms and the other from the Lorentz-violating terms. While the Lorentz-violating terms can only affect the overall amplitudes of PGWs, the parity-violating terms induce nonzero circular polarization of PGWs, i.e., the left-hand and right-hand polarization modes of GWs have different amplitudes.

Gravitational waves effects in a Lorentz–violating scenario

This paper focuses on how the production and polarization of gravitational waves are affected by spontaneous Lorentz symmetry breaking, which is driven by a self–interacting vector field. Specifically, we examine the impact of a smooth quadratic potential and a non–minimal coupling, discussing the constraints and causality features of the linearized Einstein equation. To analyze the polarization states of a plane wave, we consider a fixed vacuum expectation value (VEV) of the vector field. Remarkably, we verify that a space–like background vector field modifies the polarization plane and introduces a longitudinal degree of freedom. In order to investigate the Lorentz violation effect on the quadrupole formula, we use the modified Green function. Finally, we show that the space–like component of the background field leads to a third–order time derivative of the quadrupole moment, and the bounds for the Lorentz–breaking coefficients are estimated as well.

Gauge-invariant formulation for the gravitational wave equations

A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization with helicity ±2, Yang’s theory with three modes of polarization with helicity ±2 and 0, and so-called ‘general metric theories’ with six modes of polarization with helicity ±2, ±1, and two 0s. To identify the polarizations of gravitational waves, it is explicitly demonstrated how the gauge-invariant approach reproduces the earlier results.

Interaction of a quantum particle with gravitational wave in modified gravity theory

We present the formal solution for a quantum mechanical particle responding to gravitational wave (GW) in the framework of modified theories of gravity (MTG) where, apart from the two standard tensorial modes of polarization of GW, we have considered an additional scalar mode. The presence of this longitudinal scalar mode makes it necessary to extend the usual two-dimensional description of matter-GW interaction to a three-dimensional one. Naturally this requires non-trivial changes in the quantum mechanical treatment which we elaborate in this paper.

Nontensorial gravitational wave polarizations from the tensorial degrees of freedom: Linearized Lorentz-violating theory of gravity

Nontensorial gravitational wave polarizations from the tensorial degrees of freedom: Linearized Lorentz-violating theory of gravity

A Superconducting Tensor Detector for Mid-Frequency Gravitational Waves: Its Multichannel Nature and Main Astrophysical Targets

Abstract Mid-frequency band gravitational-wave detectors will be complementary to the existing Earth-based detectors (sensitive above 10 Hz or so) and the future space-based detectors such as the Laser Interferometer Space Antenna (LISA), which will be sensitive below around 10 mHz. A ground-based superconducting omnidirectional gravitational radiation observatory (SOGRO) has recently been proposed along with several design variations for the frequency band of 0.1–10 Hz. For two conceptual designs of SOGRO (i.e. SOGRO and advanced SOGRO [aSOGRO]), we examine their multichannel natures, sensitivities, and science cases. One of the key characteristics of the SOGRO concept is its six detection channels. The response functions of each channel are calculated for all possible gravitational wave (GW) polarizations including scalar and vector modes. Combining these response functions, we also confirm the omnidirectional nature of SOGRO. Hence, even a single SOGRO detector will be able to determine the position of a source and polarizations of GWs, if detected. Taking into account SOGRO’s sensitivity and technical requirements, two main targets are most plausible: GWs from compact binaries and stochastic backgrounds. Based on assumptions we consider in this work, detection rates for intermediate-mass binary black holes (in the mass range of hundreds up to $10^{5}\, M_\odot$) are expected to be 0.0065–8.1 yr−1. In order to detect the stochastic GW background, multiple detectors are required. Two aSOGRO detector networks may be able to put limits on the stochastic background beyond the indirect limit from cosmological observations.

Gravitational wave polarizations with different propagation speeds

Gravitational wave polarizations with different propagation speeds

Circular Polarization of the Astrophysical Gravitational Wave Background.

The circular polarization of gravitational waves is a powerful observable to test parity violation in gravity and to distinguish between the primordial or the astrophysical origin of the stochastic background. This property comes from the expected unpolarized nature of the homogeneous and isotropic astrophysical background, contrary to some specific cosmological sources that can produce a polarized background. However, in this work we show that there is also a non-negligible amount of circular polarization in the astrophysical background, generated by Poisson fluctuations in the number of unresolved sources, which is present in the third-generation interferometers with signal-to-noise ratio larger than 2. We also explain in which cases the gravitational wave maps can be cleaned from this extra source of noise, exploiting the frequency and the angular dependence, in order to search for signals from the early Universe. Future studies about the detection of polarized cosmological backgrounds with ground- and space-based interferometers should account for the presence of such a foreground contribution.

Relativistic binary systems in scale-independent energy–momentum squared gravity

ABSTRACT In this paper, we study the gravitational-wave (GW) radiation and radiative behaviour of relativistic compact binary systems in the scale-independent energy–momentum squared gravity (EMSG). The field equations of this theory are solved approximately. The gravitational potential of a gravitational source is then obtained by considering two matter Lagrangian densities that both describe a perfect fluid in general relativity (GR). We derive the GW signals emitted from a compact binary system. The results are different from those obtained in GR. It is shown that the relevant non-GR corrections modify the wave amplitude and leave the GW polarizations unchanged. Interestingly, this modification depends on the choice of the matter Lagrangian density. This means that for different Lagrangian densities, this theory presents different predictions for the GW radiation. In this case, the system loses energy to modified GWs. This leads to a change in the secular variation of the Keplerian parameters of the binary system. In this work, we investigate the non-GR effects on the radiative parameter, that is, the first time derivative of the orbital period. Next, applying these results together with GW observations from the relativistic binary systems, we constrain/test the scale-independent EMSG theory in the strong-field regime. After assuming that GR is the valid gravity theory, as a priori expectation, we find that the free parameter of the theory is of the order 10−5 from the direct GW observation, the GW events GW190425 and GW170817, as well as the indirect GW observation, the double pulsar PSR J0737−3039A/B experiment.

Polarization of Gravitational Waves in Hybrid Metric-Palatini $$f(R)$$-Gravity

Polarization of Gravitational Waves in Hybrid Metric-Palatini $$f(R)$$-Gravity

Chiral gravitational waves in Palatini-Chern-Simons gravity

We study the parity-breaking higher-curvature gravity theory of Chern-Simons (CS), using the Palatini formulation in which the metric and connection are taken to be independent fields. We first show that Palatini-CS gravity leads to first-order derivative equations of motion and thus avoid the typical instabilities of CS gravity in the metric formalism. As an initial application, we analyze the cosmological propagation of gravitational waves (GWs) in Palatini-CS gravity. We show that, due to parity breaking, the polarizations of GWs suffer two effects during propagation: amplitude birefringence (which changes the polarization ellipticity) and velocity birefringence (which rotates the polarization plane). While amplitude birefringence is known to be present in CS gravity in the metric formalism, velocity birefringence is not present in metric CS gravity for high frequency waves, but now appears in Palatini-CS due to the fact that left-handed and right-handed GW polarizations have a different dispersion relation. In the approximation of small deviations from general relativity (GR), we do find however that velocity birefringence appears at least quadratically in the CS coupling parameter $\ensuremath{\alpha}$, while amplitude birefringence appears linearly in $\ensuremath{\alpha}$. This means that amplitude birefringence will be the most relevant effect in Palatini-CS and hence this model will behave similarly to metric CS. We confirm this by applying current constraints on amplitude and velocity birefringence to Palatini-CS, and showing that those from amplitude birefringence give the tightest bounds.

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.

Inspiral gravitational waveforms from compact binary systems in Horndeski gravity

In a subclass of Horndeski theories with the speed of gravity equivalent to that of light, we study gravitational radiation emitted during the inspiral phase of compact binary systems. We compute the waveform of scalar perturbations under a post-Newtonian expansion of energy-momentum tensors of pointlike particles that depend on a scalar field. This scalar mode not only gives rise to breathing and longitudinal polarizations of gravitational waves, but it is also responsible for scalar gravitational radiation in addition to energy loss associated with transverse and traceless tensor polarizations. We calculate the Fourier-transformed gravitational waveform of two tensor polarizations under a stationary phase approximation and show that the resulting waveform reduces to the one in a parametrized post-Einsteinian (ppE) formalism. The ppE parameters are directly related to a scalar charge in the Einstein frame, whose existence is crucial to allow the deviation from general relativity (GR). We apply our general framework to several concrete theories and show that a new theory of spontaneous scalarization with a higher-order scalar kinetic term leaves interesting deviations from GR that can be probed by the observations of gravitational waves emitted from neutron star--black hole binaries. If the scalar mass exceeds the order of typical orbital frequencies $\ensuremath{\omega}\ensuremath{\simeq}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{eV}$, which is the case for a recently proposed scalarized neutron star with a self-interacting potential, the gravitational waveform practically reduces to that in GR.

Landau damping for gravitational waves in parity-violating theories

We discuss how tensor polarizations of gravitational waves can suffer Landau damping in the presence of velocity birefringence, when parity symmetry is explicitly broken. In particular, we analyze the role of the Nieh-Yan and Chern-Simons terms in modified theories of gravity, showing how the gravitational perturbation in collisionless media can be characterized by a subluminal phase velocity, circumventing the well-known results of General Relativity and allowing for the appearance of the kinematic damping. We investigate in detail the connection between the thermodynamic properties of the medium, such as temperature and mass of the particles interacting with the gravitational wave, and the parameters ruling the parity violating terms of the models. In this respect, we outline how the dispersion relations can give rise in each model to different regions of the wavenumber space, where the phase velocity is subluminal, superluminal or does not exist. Quantitative estimates on the considered models indicate that the phenomenon of Landau damping is not detectable given the sensitivity of present-day instruments.

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.

Polarizations of gravitational waves in the bumblebee gravity model

Lorentz violation modifies the dispersion relation of gravitational waves (GWs), and induces birefringence and anisotropy in propagation. Our study shows that Lorentz violation can also activate multiple polarizations of GWs. We use the gauge invariants to investigate the polarizations of GWs in the bumblebee gravity model, and obtain the following results. (i) For a vector background ${b}^{\ensuremath{\mu}}$ with only a nonzero temporal component ${b}^{t}$, there are five independent propagating degrees of freedom (d.o.f.), which is similar to the Einstein-\ae{}ther theory. (ii) The presence of a spatial component in the background defines a preferred spatial direction which breaks rotational symmetry. We denote $\stackrel{^}{\mathbit{b}}$ as the direction of the spatial part of the background and ${b}_{s}$ as its length. If GWs propagate along $\stackrel{^}{\mathbit{b}}$, the polarization content is similar to the purely timelike case. (iii) If the propagation direction of GWs is separated by an angle $\ensuremath{\beta}$ to $\stackrel{^}{\mathbit{b}}$, and $\ensuremath{\beta}=\mathrm{arccos}({b}^{t}/{b}_{s})$, there are only two tensor polarizations. (iv) If $\ensuremath{\beta}\ensuremath{\ne}\mathrm{arccos}({b}^{t}/{b}_{s})$, there are only two independent d.o.f., and the vector and scalar modes degenerate with the tensor modes. The tensor perturbations can activate a mixture of all six polarizations simultaneously. Finally, we point out the difference in GWs between the bumblebee gravity model and the minimal Standard-Model Extension framework in the linearized regime. Current observations have placed stringent constraints on the anisotropy induced by the background, while our theoretical study still reveals some novel phenomena and provides more understanding about the interaction between the Lorentz-violating vector field and gravity.