QUALITATIVE-ANALYSIS OF SOFT INFLATION

In this paper we perform a qualitative analysis of the dynamical system resulting from the soft inflation scenario. This allows us to examine the various types of asymptotic behavior displayed by the system; we pay particular attention to the inflationary solutions given by Berkin, Maeda, and Yokoyama [Phys. Rev. Lett. 65, 141 (1990)]. We find that as phi --> infinity, no unique attracting critical point exists, but rather there exists a higher-dimensional set of critical points. It is shown that the solution given by Berkin, Maeda, and Yokoyama is representative of a class of solutions which asymptotically undergoes power-law inflation. Under the assumption that new inflation occurs, we show that, asymptotically, there exists a global attractor. Under the assumption that chaotic inflation occurs, we show that there exists an attractor for finite values of the field phi and that solutions which inflate will experience infinitely many inflationary eras.