Dynamics of the inflationary flow equations

We present a dynamical analysis of the inflationary flow equations. Our technique uses the Hubble jerk parameter xi=(m(Pl)(4)/16 pi(2))H-2(dH/d phi d(3)H/d phi(3)) (where H is the Hubble parameter and phi the inflaton) as a discriminant of stability of fixed points. The results of the analysis are used to explain qualitatively the distribution of various observable parameters (e.g. the tensor-scalar ratio, r, and scalar spectral index, n(s)) seen in numerical solutions of the flow equations using stochastic initial conditions. Finally, we give a physical interpretation of the flow in phase-space in terms of slow-roll motion of the inflaton.