Abstract
According to the theory of scale relativity, dark matter halos can be described through a generalized Schrödinger equation, involving a logarithmic non-linearity associated with an effective temperature and a source of dissipation. This wave equation can be written, via the Madelung transformation, in the form of a quantum hydrodynamic model which, once coupled to the Poisson equation, is used herein to study the Jeans gravitational instability. We consider the two cases of a static and uniform unperturbed background and the generalization including the effect of Universe expansion on the zeroth-order dynamics. In each case, the stability is ensured by the effective temperature and nonlocality effects acting against gravitational forces, whereas the dissipation source damps the density contrast evolution without modifying the threshold value of the Jeans wave number.
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