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.

Backreaction inhomogeneities in the cosmological parameter evolution via a noncommutative fluid

“…The prevalent idea is that close to the big bang era, the energy density or dimension of the universe were (presumably) around Planck scale so that NC could have impacted directly but its indirect impact can be felt at present time in low-energy cosmology in the form of anisotropies in CMB or (as pointed out here) in direction-dependent effective curvature or energy content. It is worthwhile to emphasize that introduction of NC effects from a noncommutative fluid perspective, as in the present work, is complete since the NC extension of fluid has been a recent development, initiated by us [1,2,5].…”

“…(b) We, on the other hand, follow a new approach, initiated by us for the first time in [1,2,5] exploiting ideas provided in [3]. Indeed, this is possible due to the unique feature of fluid where, on one hand in the Lagrangian framework it can be interpreted as a collection of discrete particles whereas on the other hand in the Hamiltonian (or Eulerian) framework it is considered as a continuum field theory comprising of ρðxÞ, v i ðxÞ, the Eulerian field d.o.f.…”

“…The new system involves a constant antisymmetric NC parameter θ ij ¼ −θ ji and reduces smoothly to the conventional fluid model for θ ij → 0. Several novel and interesting properties of the NC model were revealed in [2] (see also [5]). In the present paper, we have extended the previous work [2] to include fluid vorticity but more importantly we have studied implications of the NC fluid model in cosmology.…”

Note on Morita Inequality for Planar Noncommutative Inverted Oscillator

“…In Morita's paper [2,3] it has been shown that in Fermi fluid, consisting of non-relativistic fermions obeying the canonical fluid equations (continuity and Euler equations with characteristic pressure term), acoustic Hawking radiation appears above a critical fluid velocity. We have constructed noncommutative extensions of ideal fluid model in a series of earlier works [11,12] and it would indeed be worthwhile to test Morita's conjecture in such system.…”