Correspondence between loop and brane cosmology

Braneworld scenarios are motivated by string/M-theory and can be characterized by the way in which they modify the conventional Friedmann equations of Einstein gravity. An alternative approach to quantum gravity, however, is the loop quantum cosmology program. In the semi-classical limit, the cosmic dynamics in this scenario can also be described by a set of modified Friedmann equations. We demonstrate that a dynamical correspondence cm be established between these two paradigms at the level of the effective field equations. As concrete examples of this correspondence, we illustrate the relationships between different cosmological backgrounds representing scaling solutions.