The conformal group SO(4,2) and Robertson-Walker spacetimes

The Robertson-Walker spacetimes are conformally flat and so are conformally invariant under the action of the Lie group S O (4, 2), the conformal grou p of Minkowski spacetime. We find a local coordinate transformation allowin g the Robertson-Walker metric to be written in a manifestly conformally fla t form for all values of the curvature parameter k continuously and use thi s to obtain the conformal Killing vectors of the Robertson-Walker spacetime s directly from those of the Minkowski spacetime. The map between the Minko wski and Robertson-Wallcer spacetimes preserves the structure of the Lie al gebra so(4, 2). Thus the conformal Killing vector basis obtained does not d epend upon k, but has the disadvantage that it does not contain explicitly a basis far the Killing vector subalgebra. We present an alternative set of bases that depend (continuously) on k and contain the Killing Vector basis as a sub-basis (these are compared with a previously published basis). In particular, bases are presented which include the Killing vectors for all R obertson-Walker spacetimes with additional symmetry including the Einstein static spacetimes and the de Sitter family of spacetimes, where the basis d epends on the Ricci scalar R.