1304.7470 (Mustapha Azreg-Aïnou)

Phase-space analysis of the cosmological 3-fluid problem: Families of
attractors and repellers    [PDF]

Mustapha Azreg-Aïnou

We perform a phase-space analysis of the cosmological 3-fluid problem consisting of a barotropic fluid with an equation-of-state parameter $\gamma-1$, a pressureless dark matter fluid, plus a scalar field $\phi$ (representing dark energy) coupled to exponential potential $V=V_0\exp{(-\kappa\lambda\phi)}$. Besides the potential-kinetic-scaling solutions, which are not the unique late-time attractors whenever they exist for $\lambda^2\geq 3\ga$, we derive new attractors where both dark energy and dark matter coexist and the final density is shared in a way independent of the value of $\ga >1$. The case of a pressureless barotropic fluid ($\ga=1$) has a one-parameter family of attractors where all components coexist. New one-parameter families of matter-dark matter saddle points and kinetic-matter repellers exist. We investigate the stability of the ten critical points by linearization and/or Lyapunov's Theorems and a variant of the theorems formulated in this paper.

View original: http://arxiv.org/abs/1304.7470