Noncommutative fluid and Growing Modes of Inhomogeneity in (Newtonian) Cosmology

Abstract

Time evolution of modes of density contrast, in particular the growing modes, dictate the structure formation in Universe. In this paper we explicitly show how (spatial) Non-Commutativity (NC) can affect the behavior of the modes, that is we compute NC corrected power law profiles of the density contrast modes. We develop a generalized fluid model that lives in NC space. The dynamical equations of fluid, namely the continuity and Euler equations receive NC contributions. When mapped to comoving coordinates these generate the NC extended versions of continuity and Friedmann equations for cosmology. Introducing cosmological perturbations finally yield the NC corrected evolution of density contrast modes. The construction of the NC fluid model from first principles and development of the formal aspects of its Hamiltonian formulation have been presented in the first part.