First Order Inflation in General Relativity

I give a general formulation of the constraints on models of inflation ended by a first order phase transition arising from the requirement that they do not produce too many large (observable) true vacuum voids – the big bubble problem'. It is shown that this constraint can be satisfied by a simple model in Einstein gravity -- a variant of hybrid’ or false vacuum' inflation. (Talk presented at Birth of the Universe’ workshop Rome, May 1994)