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

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Abstract
We reconsider the problem of gravitational structure formation inside and outside general relativity (GR), in both the weakly and strongly nonlinear 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 these predictions are when using a nonstandard 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 ω, a nonstandard parameterization of the Hubble law, H2 = a-3(1+), or a nonstandard cosmic equation of state p = γρ, where γ can be chosen irrespective of the cosmological parameters (ΩM and ΩΛ). We present some preliminary bounds on γ, ω, and from observations of the skewness and kurtosis in the Automated Plate Measuring (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 nonlinear growth will place strong constraints on such variations from the standard paradigm.