Stability properties of some perfect fluid cosmological models

Flat Friedmann-Robertson-Walker (FRW) perfect fluid cosmologies can be reproduced as particular solutions of suitable field-theoretical models. Here we investigate the stability of perfect fluid model trajectories with respect to sets of trajectories of the corresponding field models having generic initial conditions. It is shown that the trajectories of barotropic perfect fluid models and those of the Chaplygin gas model are stable. The total probability to reach the Chaplygin gas regime early enough to achieve a matter dominated stage having a realistic duration is calculated for a scalar field model assuming a natural measure in the space of initial conditions taken near a cosmological singularity. An example is presented of a two-fluid cosmological model where the stability is partially absent.

Figure 1

The dependence of $x/h^4$ for different initial values ${\varphi }_0$ and ${\dot{\varphi }}_0$.

Figure 2

The dependence of $x/h^4$ for different initial values ${\varphi }_0$ and ${\dot{\varphi }}_0$: some details.