GAUGE-INVARIANT COSMOLOGICAL PERTURBATIONS AND THE SPECTRUM OF PRIMEVAL DENSITY-FLUCTUATIONS

Fluctuation-dissipation theorems of the Landau-Lifshitz type are appli ed to cosmological perturations about a homogeneous and isotropic back ground universe. A gauge-invariant perturbation theory is used to desc ribe dissipative effects due to shear viscosity and bulk viscosity and the corresponding random fluctuations. All basic gauge-invariant quan tities are physically identified on comoving hypersurfaces. The spectr um of adiabatic energy density fluctuations on superhorizon scales is calculated. A k4 power spectrum (k = comoving wave number) is shown to be a necessary consequence of a nonvanishing shear viscosity in the e arly universe with an equation of state p = epsilon/3. Bulk viscosity is connected with a k-independent spectrum. The possible relevance of this spectrum for the theory of galaxy formation is discussed and its relation to the Harrison-Zel'dovich spectrum is clarified.