Non-Linear gravitational growth of large scale structures inside and outside standard Cosmology

We reconsider the problem of gravitational structure formation inside and outside General Relativity (GR), both in the weakly and strongly non-linear regime. We show how these regimes can be explored observationally through clustering of high order cumulants and through the epoch of formation, abundance and clustering of collapse structures, using Press-Schechter formalism and its extensions. We address the question of how different are these predictions when using a non-standard theory of Gravity. We study examples of cosmologies that do not necessarily obey Einstein's field equations: scalar-tensor theories (STT), such as Brans-Dicke (BD), parametrized with $\omega$, a non-standard parametrisation of the Hubble law, $H^2= a^{-3(1+\epsilon)}$, or a non-standard cosmic equation of state $p=\gamma\rho$, where $\gamma$ can be chosen irrespective of the cosmological parameters ($\Omega_M$ and $\Omega_\Lambda$). We present some preliminary bounds on $\gamma$, $\omega$ and $\epsilon$ from observations of the skewness and kurtosis in the APM Galaxy Survey. This test is independent of the overall normalization of rms fluctuations. We also show how abundances and formation times change under these assumptions. Upcoming data on non-linear growth will place strong constraints on such variations from the standard paradigm.