Abstract
We present a general relativistic version of the self-gravitating fluid model for the dark sector of the Universe (darkon fluid) introduced in Stichel and Zakrzewski (Phys Rev D 80:083513, 2009) and extended and reviewed in Stichel and Zakrzewski (Entropy 15:559, 2013). This model contains no free parameters in its Lagrangian. The resulting energy-momentum tensor is dustlike with a nontrivial energy flow. In an approximation valid at sub-Hubble scales we find that the present-day cosmic acceleration is not attributed to any kind of negative pressure but it is due to a dynamically determined negative energy density. This property turns out to be equivalent to a time-dependent spatial curvature. The obtained cosmological equations, at sub-Hubble scales, agree with those of the nonrelativistic model but they are given a new physical interpretation. Furthermore, we have derived the self-consistent equation to be satisfied by the nonrelativistic gravitational potential produced by a galactic halo in our model from a weak-field limit of a generalized Tolman–Oppenheimer–Volkoff equation.
Highlights
It is pretty clear that the present Universe undergoes a phase of accelerated expansion
All of these data are in good agreement with a -cold dark matter (CDM) cosmology
One can find in the literature a large number of papers explaining either the accelerated expansion and/or dark matter by changing either the geometrical part of Einstein’s field equations (EFEs) or the matter part
Summary
It is pretty clear that the present Universe undergoes a phase of accelerated expansion (see the recent reviews [1,2]). On the other hand there exists overwhelming evidence for the existence of gravitational effects on all cosmological scales (termed “dark matter”) which cannot be explained by the gravitation of standard matter in the framework of general relativity (see the review [3]) All of these data are in good agreement with a -cold dark matter (CDM) cosmology (see [1,2] and the literature cited therein). Such a model containing no new constants in its Lagrangian and based on Galilean symmetry (minimal gravitational coupling of massless Galilean particles in agreement with the equivalence principle) has been presented in [8], further developed in [9,10] and reviewed and extended in [11] This nonrelativistic, unified model for the dark sector of the Universe is an exotic fluid model, termed darkon fluid model, which contains beside the standard hydrodynamic fields a new vector field q(x, t). The aim of the present paper is to present a general relativistic version of this model and to relate some approximate solutions of it to the corresponding solutions of its nonrelativistic counterpart
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