Quasiattractor dynamics of lambda-phi^4-inflation
  At high e-foldings of expansion, the inflation with the quartic potential exhibits the parametric attractor governed by the slowly running Hubble rate. This quasiattractor simplifies the analysis of predictions for the inhomogeneity generated by the quantum fluctuations of inflaton. The method reveals the connection of inflation e-folding with general parameters of preheating regime in various scenarios and observational data. 
V. V. Kiselev, S. A. Timofeev