A classical treatment of the problems of dark energy, dark matter, and accelerating expansion

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The dynamical equivalence with geodesic motions of the isentropic hydrodynamical flows, in the interior of a bounded gravitating perfect-fluid source, implies that the baryonic mass of a cosmological or astrophysical structure can be larger than its observationally determined mass. This can provide a classical explanation of the problems of the missing mass and of the flat rotation curves of disc galaxies.
The generalized mass density producing the above geodesic motions can be either positive, or negative, or even vanish, implying the possibility of a spatially increasing, or decreasing, or even vanishing acceleration, depending on the distance from the center of the source as compared to the inversion distance. The extra ingredient to the generalized mass density, stemming from the source's internal physical characteristics, results in an extra, negative mass, beyond the baryonic mass of the source, which can be larger than the baryonic mass.
The above negative extra mass, specifically in the case of a supercluster of galaxies and in accordance with the WMAP observational data, can give a clear and precise physical meaning to the notions of dark energy, dark matter, and baryonic mass of a supercluster, which amount to, approximately, 77%, 18%, and 5%, respectively, of the supercluster's total mass. This interpretation of the WMAP data is in accordance with a hot and extended supercluster of galaxies, as the manifestation of the cosmic-structure building and as a typical picture of the Universe, contributes to the clarification of the composition of the Cosmos, and excludes the existence of third ( and higher)-order clusters of galaxies.
Treating the cosmological constant in the general-relativistic field equations as a source, in the form of a perfect fluid, the Λ-fluid, the cosmological constant does not prove to be really a constant, provided that the hydrodynamic flows in the Λ-fluid are not isentropic. This dictates the possibility of defining classically and for every structure its cosmological function. The cosmological function proves to share the numerical value and the basic properties of the cosmological constant, giving to the latter a clear physical meaning. Thus, the above unified scheme can also provide answers to problems, like repulsive gravity, accelerating/decelerating expansion of the Universe, stop-and-go Universe, Big Rip, and, finally, it predicts the existence of non-cosmological run-away motions at the inversion distance and beyond it.

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