On the inflationary flow equations

TL;DR

The paper characterizes inflationary flow equations, showing they do not directly implement inflationary dynamics but can generate a broad class of slow-roll models via a function $\epsilon(\phi)$. It derives a closed-form analytic solution for the truncated flow system, obtaining a polynomial form for $H(\phi)$ and the corresponding potential $V(\phi)$, and identifies two late-time attractors: a negative potential ending inflation or a positive minimum leading to eternal inflation. The work also discusses alternative stochastic-model-building strategies that bypass the flow formalism, highlighting that using $V(\phi)$ or directly constructing $\epsilon(\phi)$ may be more direct and informative. Altogether, the results urge caution in interpreting flow-equation outputs as representative of inflationary dynamics and emphasize that the flow method is primarily an algorithm for generating candidate models rather than a dynamical framework.

Abstract

I explore properties of the inflationary flow equations. I show that the flow equations do not correspond directly to inflationary dynamics. Nevertheless, they can be used as a rather complicated algorithm for generating inflationary models. I demonstrate that the flow equations can be solved analytically and give a closed form solution for the potentials to which flow equation solutions correspond. I end by considering some simpler algorithms for generating stochastic sets of slow-roll inflationary models for confrontation with observational data.