General relativistic, nonstandard model for the dark sector of the Universe

Stichel P, Zakrzewski WJ. General relativistic, nonstandard model for the dark sector of the Universe. The European Physical Journal C. 2015;75(1): 9.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