The AdS/CFT correspondence has emerged as an extremely powerful tool for understanding quantum gravity. I will review recent work with Craps and Hertog applying the correspondence to the simplest AdS^5 x S^5 setup, with generalised boundary conditions which allow nontrivial cosmological evolution. The result of unitary evolution in the dual field theory is a big crunch/big bang transition. Furthermore, the approximate conformal symmetry of the dual theory leads to an approximately scale-invariant spectrum of stress-energy perturbations on the boundary.