title: Quantum cosmology and conformal invariance.
abstract: According to Belinsky, Khalatnikov, and Lifshitz, gravity near a spacelike singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal mechanical models first introduced by de Alfaro, Fubini, and Furlan (DFF). The deformation used by DFF to render the spectrum discrete corresponds to a negative cosmological constant. The wave function of the Universe is the zero-energy eigenmode of the Hamiltonian, or the spherical vector of the representation of the conformal group SO(1,2). A new class of conformal quantum mechanical models with enhanced ADE symmetry is constructed, based on the quantization of nilpotent coadjoint orbits.
authors.affiliation: LPTHE, Universités Paris VI et VII, 4 Place Jussieu, 75252 Paris CEDEX 05, France. pioline@lpthe.jussieu.fr
authors.forename: B
authors.initials: B
authors.lastname: Pioline
authors.forename: A
authors.initials: A
authors.lastname: Waldron