Here is a link to Sidney Coleman's seminal paper Fate of the false vacuum: Semiclassical theory in the KEK library. He discusses a setting that is not eternal inflation, but where the false vacuum has zero energy density and essentially gives Minkowski space as the solution. In figure 4 you can see exactly the acceleration of the wall mentioned by @kimbyd. Side note: This paper contains one of my favourite quotes across all physics papers that I have read. It highlights a somewhat morbid sense of humour in Coleman (my clarifications in square brackets): Edit: Here is a link to the same paper from Princeton with much nicer formatting.