Large scale structure in the weakly non-linear regime

Is gravitational growth responsible for the observed large scale structure in the universe? Do we need non-gaussian initial conditions or non-gravitational physics to explain the large scale features traced by galaxy surveys? I will briefly revise the basic ideas of non-linear perturbation theory (PT) as a tool to understand structure formation, in particular through the study of higher order statistics, like the skewness and the 3-point function. Contrary to what happens with the second order statistics (the variance or power-spectrum), this test of gravitational instability is independent of the overall amplitude of fluctuations and of cosmic evolution, so that it does not require comparing the clustering at different redshifts. Predictions from weakly non-linear PT have been compared with observations to place constraints on our assumptions about structure formation, the initial conditions and how galaxies trace the mass.