negative and the positive time branch). This behaviour will also be confirmed in the explicit examples. Further note that the potential  consists of a sum of positive terms. Therefore, one expects the modes ${\bf P}_i\cdot\bph$ to roll up the exponential slope at early time, then turn around and roll down at late time. In other words, the exponentials $\exp ({\bf
P}_i\cdot\bph )$ decrease both in the past and in the future, at least if they explicitly appear in $V$, due to their associated integration constants $\z_i$ being non-zero. Hence, for the moduli that are not completely frozen, the associated relative volumes of the blow-ups, $\e_{(\t ,n)}$, always increases asymptotically at early and late times. We will confirm this general feature explicitly in our examples.

A universal solution
====================

As a warm-up, we would first like to consider a universal solution where all bulk moduli and all blow-up moduli evolve in the same way. It appears that a natural way to obtain such a solution is to start with an Ansatz where the seven bulk moduli are equal, that is where there is only a single breathing mode. However, it turns out that such an Ansatz is incompatible with the equations 