  A detailed examination of the Killing equations in Robertson-Walker
coordinates shows how the addition of matter and/or radiation to a de Sitter
Universe breaks the symmetry generated by four of its Killing fields. The
product U = (a^2)(dH/dt) of the squared scale parameter by the time-derivative
of the Hubble function encapsulates the relationship between the two cases: the
symmetry is maximal when U is a constant, and reduces to the six-parameter
symmetry of a generic Friedmann-Robertson-Walker model when it is not. As the
fields physical interpretation is not clear in these coordinates, comparison is
made with the Killing fields in static coordinates, whose interpretation is
made clearer by their direct relationship to the Poincare group generators via
Wigner-Inonu contractions.

General Relativity and Quantum Cosmology