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 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.