5.7.4. Open inflation
In the early 1990s, in the face of ever increasing evidence of a sub-critical matter density in the Universe, interest was refocussed on an idea which defies the original inflationary motivation and gives rise to a homogeneous but open Universe from inflation. (6) Often in the past it has been declared that this is either impossible or contrived; however, it can be readily achieved in models with quantum tunnelling from a false vacuum (a metastable state) followed by a second inflationary stage.  The tunnelling creates a bubble, and, incredibly, the region inside the expanding bubble looks just like an open Universe, with the bubble wall corresponding to the initial (coordinate) singularity. These models are normally referred to as `open inflation' or `single-bubble' models. So far it has turned out that such models are not all that easy to construct.
These models are already very different from traditional inflation models, and subsequently an even bolder idea has been proposed,  that an open Universe can be created via `tunnelling from nothing' rather than from a pre-existing inflationary phase. As I write this remains controversial.
While both these types of open inflation models remain viable, they are considerably more complex than the standard inflation models, and at the moment not that well motivated as although observations continue to favour a low matter density, they also favour spatial flatness reintroduced by a cosmological constant. Therefore from now on I will restrict discussion to the single-field chaotic inflation models.
6 That is, a
genuinely open Universe with hyperbolic geometry and no cosmological
6 That is, a genuinely open Universe with hyperbolic geometry and no cosmological constant.