This work proposes a new measure of inflation, based upon contraction of the comoving Hubble length as opposed to the usual $e$-foldings of physical expansion, and derives relevant formulae from an infinite hierarchy of slow-roll parameters.
This work constructs a family of exact solutions to the equations of motion with potentials resembling the above form and demonstrates their inflationary nature; deflationary and conflationary cosmological behaviours are also defined and identified.
Analysing the behaviour of inflationary universe models at the extrema of $\phi$ derives sufficient constraints on the parameter space such that inflation may occur as both an early and late-time phenomenon.