Spontaneous Production of the Zel'dovich Spectrum of Cosmological Fluctuations

The spectrum of initial cosmological perturbations posited by Zel'dovich and co-workers for the "pancake theory" of galaxy formation has (i) adiabatic perturbations only, and (ii) constant perturbation amplitude on all scales at their respective horizon times. Assumption (i) has recently been shown to follow from grand unified gauge theories. This paper shows that assumption (ii) may also be a consequence of spontaneous symmetry-breaking at sufficiently high temperatures. In this case the Universe may have been exactly Friedmannian originally. In a classical, U(1) Abelian Higgs model, the scale-independent dimensionless size of perturbations is here calculated to be δT00/T00 ∼ (8π/3)(Tc/m*)2 where m* is the Planck mass (1019 GeV) and Tc is the critical temperature of spontaneous symmetry-breaking, related to the mass of the gauge boson of the symmetry group. For the pancake model, one needs Tc ∼ 1017 GeV.