ar X iv : g r - qc / 0 50 90 03 v 3 3 0 A ug 2 00 7 Primeval symmetries

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 Ḣ 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 6-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 Poincaré group generators via Wigner-Inönü contractions.