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. 
Edmund J. Copeland, Seung-Joo Lee, James E. Lidsey, Shuntaro Mizuno