Generalized models of unified dark matter (DM) and dark energy (DE) in the context of Two Measure Theories and of dynamical spacetime theories are obtained. In Two Measure Theories, one uses metric independent volume elements and this allows to construct unified DM and DE, where the cosmological constant appears as an integration constant associated to the equation of motion of the measure fields. The dynamical spacetime theories generalize the Two Measure Theories by introducing a vector field whose equation of motion guarantees the conservation of a certain energy–momentum tensor, which may be related, but in general is not the same as the gravitational energy–momentum tensor. By considering the dynamical space field appearing in another part of the action (apart from the coupling to the energy–momentum tensor), we can obtain noncovariant energy–momentum conservation. Then, the dynamical spacetime theory becomes a theory of diffusive unified DE and DM. The nonconserved energy–momentum tensors lead at the end to a formulation of interacting DE–DM models in the form of a diffusive type interacting unified DE and DM scenario. We solved analytically the theories for asymptotic solution, and we show that the [Formula: see text]CDM is a fixed point of these theories at large times.
Energy-momentum tensor for scalar fields coupled to the dilaton in two dimensions