Gravitational wave modes in matter Garg, Deepen; Dodin, I.Y.
Journal of Cosmology and Astroparticle Physics,
08/2022, Letnik:
2022, Številka:
8
Journal Article
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Abstract
A general linear gauge-invariant equation for dispersive gravitational waves (GWs) propagating in matter is derived. This equation describes, on the same footing, both the usual tensor modes ...and the gravitational modes strongly coupled with matter. It is shown that the effect of matter on the former is comparable to diffraction and therefore negligible within the geometrical-optics approximation. However, this approximation is applicable to modes strongly coupled with matter due to their large refractive index. GWs in ideal gas are studied using the kinetic average-Lagrangian approach and the gravitational polarizability of matter that we have introduced earlier. In particular, we show that this formulation subsumes the kinetic Jeans instability as a collective GW mode with a peculiar polarization, which is derived from the dispersion matrix rather than assumed a priori. This forms a foundation for systematically extending GW theory to GW interactions with plasmas, where symmetry considerations alone are insufficient to predict the wave polarization.
Abstract
In linearized gravity with distributed matter, the background metric has no generic symmetries, and decomposition of the metric perturbation into global normal modes is generally ...impractical. This complicates the identification of the gauge-invariant part of the perturbation, which is a concern, for example, in the theory of dispersive gravitational waves (GWs) whose energy–momentum must be gauge-invariant. Here, we propose how to identify the gauge-invariant part of the metric perturbation and the six independent gauge invariants
per se
for an arbitrary background metric. For the Minkowski background, the operator that projects the metric perturbation on the invariant subspace is proportional to the well-known dispersion operator of linear GWs in vacuum. For a general background, this operator is expressed in terms of the Green’s operator of the vacuum wave equation. If the background is smooth, it can be found asymptotically using the inverse scale of the background metric as a small parameter.
Abstract
Modeling the propagation of gravitational waves (GWs) in media other than vacuum is complicated by the gauge freedom of linearized gravity in that, once nonlinearities are taken into ...consideration, gauge artifacts can cause spurious acceleration of the matter. To eliminate these artifacts, we propose how to keep the theory of dispersive GWs gauge-invariant beyond the linear approximation and, in particular, obtain an unambiguous gauge-invariant expression for the energy–momentum of a GW in a dispersive medium. Using analytic tools from plasma physics, we propose an exactly gauge-invariant ‘quasilinear’ theory, in which GWs are governed by linear equations and also affect the background metric on scales large compared to their wavelength. As a corollary, the gauge-invariant geometrical optics of linear dispersive GWs in a general background is formulated. As an example, we show how the well-known properties of vacuum GWs are naturally and concisely yielded by our theory in a manifestly gauge-invariant form. We also show how the gauge invariance can be maintained within a given accuracy to an arbitrary order in the GW amplitude. These results are intended to form a physically meaningful framework for studying dispersive GWs in matter.
Recent detection of electromagnetic (EM) waves along with gravitational waves (GWs) has ushered in the era of multimessenger astronomy. On one hand, it has the potential to yield precious information ...about the environment of the corresponding astrophysical compact objects, and on the other hand, it can greatly complement the “standard siren” technique of using GWs in cosmology, and benefit our understanding about the early Universe physics. However, to fully leverage all the possible information from the correlation of GWs with EM waves, their coupling outside the vacuum modes must be considered as well, requiring a careful thorough study of the coupling of self-consistent GWs with EM plasma modes. This thesis concerns developing such a formalism to study the collective effects of GWs interacting with gases and plasmas. The standard approach to study GW--matter coupling is to solve Einstein--Vlasov equations, but it has proven to be prohibitively cumbersome and typically involves oversimplifications, unable to account for the collective effects. We use an alternative, variational formulation to derive the gauge-invariant wave equation for collective oscillations of the self-consistent metric, EM fields and plasma. This forms a foundation for studying GW--plasma interactions rigorously.
Abstract This paper explores the hybridization of linear metric perturbations with linear electromagnetic (EM) perturbations in non-magnetized plasma for a general background metric. The local wave ...properties are derived from first principles for inhomogeneous plasma, without assuming any symmetries of the background metric. First, we derive the effective (“oscillation-center”) Hamiltonian that governs the average dynamics of plasma particles in a prescribed quasimonochromatic wave that involves metric perturbations and EM fields simultaneously. Then, using this Hamiltonian, we derive the backreaction of plasma particles on the wave itself and obtain gauge-invariant equations that describe the resulting self-consistent gravito-electromagnetic (GEM) waves in a plasma. The transverse tensor modes of gravitational waves are found to have no interaction with the plasma and the EM modes in the geometrical-optics limit. However, for longitudinal GEM modes with large values of the refraction index, the interplay between gravitational and EM interactions in plasma can have a strong effect. In particular, the dispersion relation of the Jeans mode is significantly affected by electrostatic interactions. As a spin-off, our calculation also provides an alternative resolution of the so-called Jeans swindle.
Particles interacting with a prescribed quasimonochromatic gravitational wave (GW) exhibit secular (average) nonlinear dynamics that can be described by Hamilton's equations. We derive the ...Hamiltonian of this "ponderomotive" dynamics to the second order in the GW amplitude for a general background metric. For the special case of vacuum GWs, we show that our Hamiltonian is equivalent to that of a free particle in an effective metric, which we calculate explicitly. We also show that already a linear plane GW pulse displaces a particle from its unperturbed trajectory by a finite distance that is independent of the GW phase and proportional to the integral of the pulse intensity. We calculate the particle displacement analytically and show that our result is in agreement with numerical simulations. We also show how the Hamiltonian of the nonlinear averaged dynamics naturally leads to the concept of the linear gravitational susceptibility of a particle gas with an arbitrary phase-space distribution. We calculate this susceptibility explicitly to apply it, in a follow-up paper, toward studying self-consistent GWs in inhomogeneous media within the geometrical-optics approximation.
This paper explores the hybridization of linear metric perturbations with linear electromagnetic (EM) perturbations in non-magnetized plasma for a general background metric. The local wave properties ...are derived from first principles for inhomogeneous plasma, without assuming any symmetries of the background metric. First, we derive the effective (``oscillation-center'') Hamiltonian that governs the average dynamics of plasma particles in a prescribed quasimonochromatic wave that involves metric perturbations and EM fields simultaneously. Then, using this Hamiltonian, we derive the backreaction of plasma particles on the wave itself and obtain gauge-invariant equations that describe the resulting self-consistent gravito-electromagnetic (GEM) waves in a plasma. The transverse tensor modes of gravitational waves are found to have no interaction with the plasma and the EM modes in the geometrical-optics limit. However, for ``longitudinal" GEM modes with large values of the refraction index, the interplay between gravitational and EM interactions in plasma can have a strong effect. In particular, the dispersion relation of the Jeans mode is significantly affected by electrostatic interactions. As a spin-off, our calculation also provides an alternative resolution of the so-called Jeans swindle.
Modeling the propagation of gravitational waves (GWs) through matter is complicated by the gauge freedom of linearized gravity in that once nonlinearities are taken into consideration, gauge ...artifacts can cause spurious acceleration of the matter. To eliminate these artifacts, we propose how to keep the theory of dispersive GWs gauge-invariant beyond the linear approximation and, in particular, obtain an unambiguous gauge-invariant expression for the energy--momentum of a GW in dispersive medium. Using analytic tools from plasma physics, we propose an exactly gauge-invariant ``quasilinear'' theory, in which GWs are governed by linear equations and also affect the background metric on scales large compared to their wavelength. As a corollary, the gauge-invariant geometrical optics of linear dispersive GWs in a general background is formulated. As an example, we show how the well-known properties of vacuum GWs are naturally and concisely yielded by our theory in a manifestly gauge-invariant form. We also show how the gauge invariance can be maintained within a given accuracy to an arbitrary order in the GW amplitude. These results are intended to form a physically meaningful framework for studying dispersive GWs in matter.
In linearized gravity with distributed matter, the background metric has no generic symmetries, and decomposition of the metric perturbation into global normal modes is generally impractical. This ...complicates the identification of the gauge-invariant part of the perturbation, which is a concern, for example, in the theory of dispersive gravitational waves whose energy--momentum must be gauge-invariant. Here, we propose how to identify the gauge-invariant part of the metric perturbation and the six independent gauge invariants \textit{per~se} for an arbitrary background metric. For the Minkowski background, the operator that projects the metric perturbation on the invariant subspace is proportional to the well-known dispersion operator of linear gravitational waves in~vacuum. For a general background, this operator is expressed in terms of the Green's operator of the vacuum wave equation. If the background is smooth, it can be found asymptotically using the inverse scale of the background metric as a small parameter.
We study how Abelian-gauge-field production during inflation affects scalar perturbations in the case when the gauge field interacts with the inflaton directly (by means of generic kinetic and axial ...couplings) and via gravity. The homogeneous background solution is defined by self-consistently taking into account the backreaction of the gauge field on the evolution of the inflaton and the scale factor. For the perturbations on top of this background, all possible scalar contributions coming from the inflaton, the metric, and the gauge field are considered. We derive a second-order differential equation for the curvature perturbation, \(\zeta\), capturing the impact of the gauge field, both on the background dynamics and on the evolution of scalar perturbations. The latter is described by a source term in the \(\zeta\)-equation, which is quadratic in the gauge-field operators and leads to non-Gaussianities in the curvature perturbations. We derive general expressions for the induced scalar power spectrum and bispectrum. Finally, we apply our formalism to the well-known case of axion inflation without backreaction. Numerical results show that, in this example, the effect of including metric perturbations is small for values of the gauge-field production parameter \(\xi> 3\). This is in agreement with the results of previous studies in the literature. However, in the region of smaller values, \(\xi\lesssim 2\), our new results exhibit order-of-unity deviations when compared to previous results.
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