Stability of cosmological scaling solutions - art. no. 123501

We study the stability of cosmological scaling solutions within the class o f spatially homogeneous cosmological models with a perfect fluid subject to the equation of state p gamma = (gamma-1)rho(gamma) (where gamma is a cons tant satisfying 0<gamma<2) and a scalar field with an exponential potential . The scaling solutions, which are spatially flat isotropic models in which the scalar field energy density tracks that of the perfect fluid, are of p hysical interest. For example, in these models a significant fraction of th e current energy density of the Universe may be contained in the scalar fie ld whose dynamical effects mimic cold dark matter. It is known that the sca ling solutions are late-time attractors (i.e., stable) in the subclass of f lat isotropic models. We find that the scaling solutions are stable (to she ar and curvature perturbations) in generic anisotropic Bianchi models when gamma <2/3. However, when gamma>2/3, and particularly for realistic matter with gamma greater than or equal to 1, the scaling solutions are unstable; essentially they are unstable to curvature perturbations, although they are stable to shear perturbations. We briefly discuss the physical consequence s of these results. [S0556-2821(98)10920-7].