Energy injection into the early universe can induce turbulent motions of the primordial plasma, which in turn act as a source for gravitational radiation. Earlier work computed the amplitude and characteristic frequency of the relic gravitational wave background, as a function of the total energy injected and the stirring scale of the turbulence. This paper computes the frequency spectrum of relic gravitational radiation from a turbulent source of the stationary Kolmogoroff form which acts for a given duration, making no other approximations. We also show that the limit of long source wavelengths, commonly employed in aeroacoustic problems, is an excellent approximation. The gravitational waves from cosmological turbulence around the electroweak energy scale will be detectable by future space-based laser interferometers for a substantial range of turbulence parameters.

Gravitational waves potentially represent our only direct probe of the universe when it was less than one second old. In particular, first-order phase transitions in the early universe can generate a stochastic background of gravitational waves which may be detectable today. We briefly summarize the physical sources of gravitational radiation from phase transitions and present semi-analytic expressions for the resulting gravitational wave spectra from three distinct realistic sources: bubble collisions, turbulent plasma motions, and inverse-cascade helical magnetohydrodynamic turbulence. Using phenomenological parameters to describe phase transition properties, we determine the region of parameter space for which gravitational waves can be detected by the proposed Laser Interferometer Space Antenna. The electroweak phase transition is detectable for a wide range of parameters.

We show that helical turbulence produced during a first-order phase transition generates circularly polarized cosmological gravitational waves (GWs). The characteristic frequency of these GWs for an extreme case of the phase transition model is around 10 −3 -10 −2 Hz with an energy density parameter as high as 10 −12 -10 −11 . The possibility of detection is briefly discussed. Since cosmological GWs propagate without significant interaction after they are produced, once detected they should provide a powerful tool for studying the early Universe at the time of GW generation [1]. Various mechanisms for cosmological GW generation have been studied, including: quantum fluctuations during inflation [2]; bubble wall motion and collisions during phase transitions [3]; cosmological magnetic fields [4,5]; and plasma turbulence [5,6,7].In this letter we focus on polarization of cosmological GWs generated by helical stochastic turbulent motions [8,9,10]. We find that helical turbulence generates circularly polarized stochastic GWs and we compute the polarization degree. The formalism we use is general and can be applied to study the generation of stochastic GWs by any helical vector field (e.g., helical magnetic fields [10,11]). Primordial polarized GWs might be generated from quantum fluctuations accounting for the gravitational Chern-Simons term [12].GWs are sourced by the transverse and traceless part of the stress-energy tensor T µν [13]. In the case at hand T µν describes a turbulent cosmological fluid after a phase transition [3,5,6]. For spatial indices i = j, T ij (x) = (p+ρ)u i (x)u j (x), where p and ρ are the fluid pressure and energy density and u(x) is the fluid velocity. The fluid enthalpy density p+ ρ is taken to be constant throughout space. The transverse and traceless part ofwith observations we have assumed flat space sections.To model the turbulence we assume that in the early Universe at time t in (at a phase transition) liberated vacuum energy ρ vac is converted into (turbulent) kinetic energy of the cosmological plasma with an efficiency κ over a time scale τ stir on a characteristic source length scale L S [3]. After generation, the turbulence kinetic energy cascades from larger to smaller scales. The cascade stops at a damping scale, L D , where the turbulence energy is removed by dissipation. As usual, we assume that the turbulence is produced in a time much less than the Hubble time, τ stir ≪ 1/H in -here H in is the Hubble parameter at t in - [5,6], and therefore we ignore the expansion of the Universe when studying the generation of GWs. In this case the GW equation of motion, in wave number space, is [13] Here G is the Newtonian gravitational constant, and3 is the Fourier transform pair of the tensor metric perturbation which is defined h ij = δg ij (h ii = 0 and h ijk j = 0). We use natural units = 1 = c, physical/proper wave numbers (not comoving ones), and an overdot denotes a derivative with respect to time t.Stochastic turbulent fluctuations generate stochastic GWs. Gaussian-distributed ...

We consider the generation of gravitational waves by primordial helical inverse cascade magnetohydrodynamic (MHD) turbulence produced by bubble collisions at the electroweak phase transition. We extend the previous study [1] by considering both currently discussed models of MHD turbulence. For popular electroweak phase transition parameter values, the generated gravitational wave spectrum is only weakly dependent on the MHD turbulence model. Compared to the unmagnetized electroweak phase transition case, the spectrum of MHD-turbulence-generated gravitational waves peaks at lower frequency with larger amplitude and can be detected by the proposed Laser Interferometer Space Antenna.

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Special features of magnetohydrodynamic waves linear dynamics in smooth shear flows are studied. Quantitative asymptotic and numerical analysis are performed for wide range of system parameters when basic flow has constant shear of velocity and uniform magnetic field is parallel to the basic flow. The special features consist of magnetohydrodynamic wave mutual transformation and over-reflection phenomena. The transformation takes place for arbitrary shear rates and involves all magnetohydrodynamic wave modes. While the over-reflection occurs only for slow magnetosonic and Alfvén waves at high shear rates. Studied phenomena should be decisive in the elaboration of the self-sustaining model of magnetohydrodynamic turbulence in the shear flows.

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A novel model of incompressible magnetohydrodynamic turbulence in the presence of a strong external magnetic field is proposed for explanation of recent numerical results. According to the proposed model, in the presence of the strong external magnetic field, incompressible magnetohydrodynamic turbulence becomes nonlocal in the sense that low frequency modes cause decorrelation of interacting high frequency modes from the inertial interval. It is shown that the obtained nonlocal spectrum of the inertial range of incompressible magnetohydrodynamic turbulence represents an anisotropic analogue of Kraichnan's nonlocal spectrum of hydrodynamic turbulence. Based on the analysis performed in the framework of the weak coupling approximation, which represents one of the equivalent formulations of the direct interaction approximation, it is shown that incompressible magnetohydrodynamic turbulence could be both local and nonlocal and therefore anisotropic analogues of both the Kolmogorov and Kraichnan spectra are realizable in incompressible magnetohydrodynamic turbulence.