  Making a connection between observations of cosmological correlation
functions and those calculated from theories of the early universe requires
that these quantities are conserved through the periods of the universe which
we do not understand. In this paper, the results of [0810.2831] are extended to
show that tree-approximation correlation functions of Heisenberg picture
operators for the reduced spatial metric are constant outside the horizon
during local thermal equilibrium with no non-zero conserved quantum numbers.
