Collective effects for dispersive gravitational waves in plasma

Interaction of gravitational waves (GWs) with matter could be important, for example, in the early Universe, and in the vicinity of compact GW sources where the enormous amount of energy stored in the GWs can make even a weak coupling significant. The standard approach to studying these effects is to solve Einstein--Vlasov equations, but it has proven to be prohibitively cumbersome and typically involves oversimplifications. We use an alternative, variational formulation [PRD 102, 064012 (2020); arxiv:2106.05062] to derive the gauge-invariant (GI) wave equations for collective oscillations of the self-consistent metric. We also show how to find the GI part of the metric perturbation in an arbitrary background metric (arXiv:2105.04680), and propose their GI adiabatic quasilinear theory and geometrical optics (arXiv:2106.05062; arxiv:2201.08562, to appear in JPP). This forms a foundation for describing GW--plasma interactions rigorously. For example, we show that the kinetic Jeans instability can be subsumed as a collective GW mode with a peculiar polarization, which is derived from the dispersion matrix rather than assumed a priori as usual (arXiv:2204.09095, to appear in JCAP). We also briefly discuss possible future directions and applications of this general formalism.