DYNAMICAL CRITICAL PHENOMENA AND LARGE-SCALE STRUCTURE OF THE UNIVERSE - THE POWER SPECTRUM FOR DENSITY-FLUCTUATIONS

As is well known, structure formation in the Universe at times after d ecoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar-Par isi-Zhang equation. As a consequence of the dynamical critical scaling induced by noise, these equations describe the fractal behavior obser ved at the smaller scales for the galaxy-to-galaxy correlation functio n and also the Harrison-Zel'dovich spectrum at decoupling. By a renorm alization group calculation of the two-point correlation function betw een galaxies we can account, from first principles, for the main featu res of the observed shape of the power spectrum.