Abstract
As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar-Parisi-Zhang equation. As a consequence of the dynamical critical scaling induced by noise, these equations describe the fractal behavior observed at the smaller scales for the galaxy-to-galaxy correlation function and also the Harrison-Zel'dovich spectrum at decoupling. By a renormalization group calculation of the two-point correlation function between galaxies we can account, from first principles, for the main features of the observed shape of the power spectrum.