0 1 2 3 4 5 6 7 t GLYPH<Minus> 5 0 5 10 GLYPH<CapPhi> 0 20000 40000 60000 80000 100000 t 1 1.1 1.2 1.3 1.4 1.5 1.6 GLYPH<CapPhi> FIG. 14: The plot shows φ (scaled by φ$_{0}$ ) as a function of time for φ$_{i}$ = 10 and ˙ φ$_{i}$ = 100, with H$_{false}$ = 10 $^{3}$m$_{φ}$ . There is an initial oscillatory phase since V ′′ ( φ$_{i}$ ) ≥ H 2 $_{false}$. It ends quickly as the amplitude of oscillations decreases fast due to Hubble expansion. Then the slow-roll motion begins which lasts much longer. In the second plot the slow-roll phase for the same initial conditions is depicted. It lasts very long but the field asymptotes to the point of inflection φ$_{0}$ with ˙ φ → 0. The plots are take from [90]. FIG. 15: The attractor behavior holds for a wide range of initial values of φ and ˙ φ . In the left panel the initial values of φ versus ˙ φ for H$_{false}$ = 10 $^{2}$m$_{φ}$ is shown. The dots show the initial values for which φ settles to ± φ$_{0}$ and the white bands ∩ show the critically damped regions where φ settles to zero at late times. The situation improves a lot for a larger H$_{false}$ = 10 $^{4}$m$_{φ}$ as shown in the right hand panel. The plots are symmetric under φ → − φ . Here we have shown the upper half of φ − ˙ φ plane where φ ≥ 0. The plots are take from [90]. 169