Phase space analysis of quintessence cosmologies with a double exponential potential -: art. no. 016

We use phase space methods to investigate closed, flat, and open Friedmann - Robertson - Walker cosmologies with a scalar potential given by the sum of two exponential terms. The form of the potential is motivated by the dimensional reduction of M-theory with non-trivial four-form flux on a maximally symmetric internal space. To describe the asymptotic features of run-away solutions we introduce the concept of a 'quasi fixed point'. We give the complete classification of solutions according to their late-time behaviour ( accelerating, decelerating, crunch) and the number of periods of accelerated expansion.