Generalised cosmological scaling solutions

Motivated by the recent interest in cosmologies arising from energy density modifications to the Friedmann equation, we analyse the scaling behaviour for a broad class of these cosmologies comprised of scalar fields and background barotropic fluid sources. In particular, we determine the corresponding scalar field potentials which lead to attractor scaling solutions in a wide class of braneworld and dark energy scenarios. We show how a number of recent proposals for modifying the Friedmann equation can be thought of as being dual to one another, and determine the conditions under which such dualities arise.