Evolution equation for non-linear cosmological perturbations

Ram Brustein, Antonio Riotto

Research output: Contribution to journalArticlepeer-review


We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations, with some possibly important differences. We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance.

Original languageAmerican English
Article number006
JournalJournal of Cosmology and Astroparticle Physics
Issue number11
StatePublished - 1 Nov 2011


  • cosmological perturbation theory
  • galaxy clustering
  • galaxy surveys

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics


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