Can cosmic acceleration be caused by exotic massless particles?

To describe dark energy we introduce a fluid model with no free parameter on the microscopic level. The constituents of this fluid are massless particles which are a dynamical realisation of the unextended $D=(3+1)$ Galilei algebra. These particles are exotic as they live in an enlarged phase space. Their only interaction is with gravity. A minimal coupling to the gravitational field, satisfying Einstein's equivalence principle, leads to a dynamically active gravitational mass density of either sign. A two-component model containing matter (baryonic and dark) and dark energy leads, through the cosmological principle, to Friedmann-like equations. Their solutions show a deceleration phase for the early universe and an acceleration phase for the late universe. We predict the Hubble parameter $H(z)/H_0$ and the deceleration parameter $q(z)$ and compare them with available experimental data. We also discuss a reduced model (one component dark sector) and the inclusion of radiation. Our model shows no stationary modification of Newton's gravitational potential.