Two-dimensional quantum cosmology

Two-dimensional quantum gravity coupled to conformally invariant matter with central charge c > 25 has been proposed as a toy model for quantum gravity in higher dimensions. The associated "Wheeler-DeWitt equation" is non-linear and unstable to forming a condensate of baby universes. This will occur even in the classical c → ∞ limit. Small fluctuations about this background describe the propagation of single universes and satisfy a more conventional linear Wheeler-DeWitt equation. The resulting two-dimensional cosmology depends on details of the non-linear dynamics. In particular the existence of a large-scale cosmological constant is determined by the behavior of a string theoretic tachyon potential near its minimum.