  This paper is based on a talk given by A R Liddle at the PASCOS/TEXAS meeting
in December 1992, and will appear in the proceedings. The central result is
that all known models of inflation which end in a first order phase transition
can be ruled out by combining galaxy surveys at a few tens of Mpc with the COBE
data (including the effect of gravitational waves). This conclusion is based on
the work described in A R Liddle and D H Lyth, Phys Lett B 291 (1992) 391.
