Cosmological models and renormalization group flow -: art. no. 011

We study cosmological solutions of Einstein gravity with a positive cosmological constant in diverse dimensions. These include big-bang models that re-collapse, big-bang models that approach de Sitter acceleration at late times, and bounce models that are both past and future asymptotically de Sitter. The re-collapsing and the bounce geometries are all tall in the sense that entire spatial slices become visible to a comoving observer before the end of conformal time, while the accelerating big-bang geometries can be either short or tall. We consider the interpretation of these cosmological solutions as renormalization group flows in a dual field theory and give a geometric interpretation of the associated c-function as the area of the apparent cosmological horizon in Planck units. The covariant entropy bound requires quantum erects to modify the early causal structure of some of our classical big-bang solutions.