Versal transition scenarios in inflationary cosmology: slow roll, ultra-slow roll, and oscillatory exit
We develop a physics-facing version of the persistence/transition-variety framework for scalar-field cosmology, tailored to inflationary dynamics. The guiding idea is that observationally viable inflationary models are often best understood not as single asymptotic phases but as concatenations of persistent regimes separated by universal transition episodes. In this picture, slow roll appears as a robust persistent balance, ultra-slow roll as a bottleneck passage near a nonhyperbolic organising set, and oscillatory post-inflationary behaviour as a recurrent exit sector. Using the exponential model as a reference regime atlas and the massive case as a dynamical realisation of slope drift, we show how such histories may be organised and read geometrically. The resulting framework makes explicit that the relevant regime transitions are organised precisely where hyperbolicity is lost or the spectrum crosses the imaginary axis, and are therefore invisible to a purely hyperbolic or asymptotic treatment.