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This work is a follow-up to the paper, "Numerical Relativity as a Tool forStudying the Early Universe". In this article, we determine if cosmologicalgravitational waves can be accurately extracted from a dynamical spacetimeusing an averaging process as opposed to conventional methods of gravitationalwave extraction using a complex Weyl scalar. We calculate the normalized energydensity, strain and degree of polarization of gravitational waves produced by asimulated turbulent plasma similar to what was believed to have existed shortlyafter the electroweak scale. This calculation is completed using two numericalcodes, one which utilizes full General Relativity calculations based onmodified BSSN equations while the other utilizes a linearized approximation ofGeneral Relativity. Our results show that the spectrum of gravitational wavescalculated from the nonlinear code using an averaging process are nearlyindistinguishable from those calculated from the linear code. This resultvalidates the use of the averaging process for gravitational wave extraction ofcosmological systems.

Extracting Gravitational Waves Induced by Plasma Turbulence in the Early Universe through an Averaging Process