Introduction

Our state of knowledge of the universe has improved markedly in the last twenty years. Observations of the microwave background radiation, large-scale structure and distant supernovae provide strong evidence for a universe composed of about 4% baryonic matter, 20% non-baryonic dark matter, and 76% dark energy (Spergel et al., 2007). Of the last two components, we know rather little in detail, so the obvious question for the next decades is what is the nature of the dark matter and dark energy? The last component is the most unexpected, and might correspond to Einstein's cosmological constant, or to a dynamical substance with an equation of state parameter w ≡ p/(ρc2) currently close to −1, but which may evolve with time. More intriguingly still, it might not be dark energy at all, but rather a manifestation of a law of gravity that is not Einstein's, and might be a result of a higher-dimensional universe. Dark energy and modified gravity manifest themselves in two general ways that open up possibilities for confronting theories with observation. Firstly, they affect the expansion history of the universe, and secondly they influence the growth rate of perturbations. The expansion history can be probed by observations of distant supernovae or baryon oscillations, and these are covered elsewhere in this volume. Gravitational lensing can probe both, by distorting the images of distant galaxies as the light passes through the non-uniform universe.