W. Zimdahl, GAUGE-INVARIANT COSMOLOGICAL PERTURBATIONS AND THE SPECTRUM OF PRIMEVAL DENSITY-FLUCTUATIONS, Physical review. D. Particles and fields, 48(6), 1993, pp. 2431-2442
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.