Unification of dark energy and dark matter from diffusive cosmology

Generalized ideas of unified dark matter and dark energy in the context of dynamical space time theories with a diffusive transfer of energy are studied. The dynamical space-time theories introduce a vector field whose equation of motion guarantees a conservation of a certain energy momentum tensor, which may be related, but in general is not the same as the gravitational energy momentum tensor. This particular energy momentum tensor is built from a general combination of scalar fields derivatives as the kinetic terms, and possibly potentials for the scalar field. By demanding that the dynamical space vector field be the gradient of a scalar the dynamical space time theory becomes a theory for diffusive interacting dark energy and dark matter. These generalizations produce nonconserved energy momentum tensors instead of conserved energy momentum tensors which lead at the end to a formulation for interacting dark energy and dark matter (DE-DM). We solved analytically the theories and we show that the $\mathrm{\Lambda }\mathrm{CDM}$ is a fixed point of these theories at large times. A particular case has asymptotic correspondence to previously studied non-Lagrangian formulations of diffusive exchange between dark energy and dark matter.

Figure 1

The phase portrait for the dynamical system method. In the left panel the $\tilde{\omega }=-1$ refers to dark energy and in the right panel the $\omega =-1$ refers to dark energy.

Figure 2

The numerical solution of the partial densities of the dark energy and dark matter components, for different values of the coupling ${\gamma }^2$ (which is corresponding to the diffusion constant $\sigma$).