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

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.