Unified dark energy and dark matter from dynamical spacetime

A unification of dark matter and dark energy based on a dynamical spacetime theory is suggested. By introducing a dynamical spacetime vector field χμ as a Lagrange multiplier, conservation of an energy momentum tensor T(χ)μν is implemented. This Lagrangian generalizes the "unified dark energy and dark matter from a scalar field different from quintessence" [Phys. Rev. D 81, 043520 (2010)PRVDAQ1550-799810.1103/PhysRevD.81.043520], which did not consider a Lagrangian formulation. This generalization allows the solutions which were found previously, but in addition to that also nonsingular bouncing solutions that rapidly approach to the ΛCDM model. The dynamical time vector field exactly coincides with the cosmic time for the a ΛCDM solution and suffers a slight shift (advances slower) with respect to the cosmic time in the region close to the bounce for the bouncing nonsingular solutions. In addition, we introduce some exponential potential which could enter into the T(χ)μν stress energy tensor or be coupled directly to the measure -g, giving a possible interaction between dark energy and dark matter, and could explain the coincidence problem.