Macroscopic theory of dark sector

Abstract

A simple Lagrangian with squared covariant divergence of a vector field as a kinetic term turned out an adequate tool for macroscopic description of the dark sector. The zero-mass field acts as the dark energy. Its energy-momentum tensor is a simple additive to the cosmological constant. Massive fields {\phi}_{I} with {\phi}^{K}{\phi}_{K}<0 and {\phi}^{K}{\phi}_{K}>0 describe two different forms of dark matter. The space-like ({\phi}^{K}{\phi}_{K}<0) massive vector field is attractive. It is responsible for the observed plateau in galaxy rotation curves. The time-like ({\phi}^{K}{\phi}_{K}>0) massive field displays repulsive elasticity. In balance with dark energy and ordinary matter it provides a four parametric diversity of regular solutions of the Einstein equations describing different possible cosmological and oscillating non-singular scenarios of evolution of the universe. In particular, the singular big bang turns into a regular inflation-like transition from contraction to expansion with the accelerate expansion at late times. The fine-tuned Friedman-Robertson-Walker singular solution is a particular limiting case at the boundary of existence of regular oscillating solutions in the absence of vector fields. The simplicity of the general covariant expression for the energy-momentum tensor allows to display the main properties of the dark sector analytically and avoid unnecessary model assumptions.