Dust of dark energy

We introduce a novel class of field theories where energy always flows along timelike geodesics, mimicking in that respect dust, yet which possess non-zero pressure. This theory comprises two scalar fields, one of which is a Lagrange multiplier enforcing a constraint between the other's field value and derivative. We show that this system possesses no wavelike modes but retains a single dynamical degree of freedom. Thus, the sound speed is always identically zero on all backgrounds. In particular, cosmological perturbations reproduce the standard behaviour for hydrodynamics in the limit of vanishing sound speed. Using all these properties we propose a model unifying Dark Matter and Dark Energy in a single degree of freedom. In a certain limit this model exactly reproduces the evolution history of Lambda CDM, while deviations away from the standard expansion history produce a potentially measurable difference in the evolution of structure.