2.4 are regarded as arbitrary constants. Each branch of the curve marks a transition between regions with different solution types. To show this we study the case of two dustlike fluids in detail. Thus they have a maximum and recollapse into a big crunch. Open and flat ones expand forever, the latter stopping their expansion asymptotically.
All models start with a big bang singularity.
According to Eqs. If there is no zero, then the universe starts with a big bang and expands forever. Two zeros lead to solutions with one extremum, because either both are less or both are greater than unity. Thus, crossing this curve the solutions will skip from one type to the other. Figure 2 summarizes the results for specific values .