Turbulence of Weak Gravitational Waves in the Early Universe

Abstract

We study the statistical properties of an ensemble of weak gravitational waves interacting nonlinearly in a flat space-time. We show that the resonant three-wave interactions are absent and develop a theory for four-wave interactions in the reduced case of a 2.5 þ 1 diagonal metric tensor. In this limit, where only plus-polarized gravitational waves are present, we derive the interaction Hamiltonian and consider the asymptotic regime of weak gravitational wave turbulence. Both direct and inverse cascades are found for the energy and the wave action, respectively, and the corresponding wave spectra are derived. The inverse cascade is characterized by a finite-time propagation of the metric excitations-a process similar to an explosive nonequilibrium Bose-Einstein condensation, which provides an efficient mechanism to ironing out small-scale inhomogeneities. The direct cascade leads to an accumulation of the radiation energy in the system. These processes might be important for understanding the early Universe where a background of weak nonlinear gravitational waves is expected.

Nonlinear diffusion models for gravitational wave turbulence

“…Besides the kinetic equations, the main results obtained are the derivation of its power-law (constant flux) solutions and the demonstration that we have a direct energy cascade and an explosive inverse cascade of wave action (a property of finitecapacity turbulence systems) with a priori the possibility to excite Fourier modes from the injection wavenumber k I to k = 0 in a finite time. However, and as discussed in [6], such a transfer driven by GW turbulence stops at an * sebastien.galtier@u-psud.fr † sergey.nazarenko@inphyni.cnrs.fr ‡ eric.buchlin@ias.u-psud.fr § simon.thalabard@impa.br intermediate scale where the turbulence regime becomes strong. Note that the change of regime does not preclude the possibility to extend such an inverse cascade to k = 0 in a finite time [8].…”

“…In the present paper, we propose two diffusion models for GW turbulence: a fourth-order and a second-order model which are introduced in sections II and III, respectively. Their derivation is based, in particular, on the phenomenology of wave turbulence that was introduced in [6]. Numerical simulations of the second-order diffusion model are then performed to study the form of arXiv:1809.07623v1 [gr-qc] 18 Sep 2018 the front propagation during the inverse cascade of wave action.…”

Weak‐Turbulent Theory of Wind‐Driven Sea

“…It is clear now that WTT can be used for the description of very broad class of physical phenomena, including waves in magnetohydrodynamics (Galtier et al, 2000), waves in nonlinear optics (Yousefi, 2017), gravitational waves in the Universe (de Oliveira et al, 2013;Galtier & Nazarenko, 2017), plasma waves (Balk, 2000;Yoon et al, 2016), capillary waves (Pushkarev & Zakharov, 1996;Yulin, 2017;Tran, 2017), and Kelvin waves in super-fluid helium (Lvov & Nazarenko, 2010). Nowadays, WTT is the branch of theoretical physics.…”

Numerical measurements of scaling relations in two-dimensional conformal fluid turbulence

“…[8,9]) and, through the fluid-gravity correspondence, it has found its way into the realm of fundamental gravity research [10,11]. Intriguingly, this correspondence has revealed that gravity can exhibit turbulent behavior, and studies of its possible consequences are gaining interesting momentum [12][13][14][15][16]. The understanding of turbulence in any regime is a difficult task given its intrinsic complexity, and despite a long history of efforts in the subject, our knowledge of this rich phenomenon is still incomplete.…”