Nonlinear Gravitational Growth of Large‐Scale Structures Inside and Outside Standard Cosmology

We reconsider the problem of gravitational structure formation inside andoutside General Relativity (GR), both in the weakly and strongly non-linearregime. We show how these regimes can be explored observationally throughclustering of high order cumulants and through the epoch of formation,abundance and clustering of collapse structures, using Press-Schechterformalism and its extensions. We address the question of how different arethese predictions when using a non-standard theory of Gravity. We studyexamples of cosmologies that do not necessarily obey Einstein's fieldequations: scalar-tensor theories (STT), such as Brans-Dicke (BD), parametrizedwith $\omega$, 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 andkurtosis in the APM Galaxy Survey. This test is independent of the overallnormalization of rms fluctuations. We also show how abundances and formationtimes change under these assumptions. Upcoming data on non-linear growth willplace strong constraints on such variations from the standard paradigm.Comment: 15 pages, 9 figures, LaTeX, accepted in the Astrophysical Journal. Replaced with minor changes, a new figure with Cluster Abundance predictions adde