1998/05/31 by Andrew Billyard, A. P. Billyard, A. A. Coley +1 · 5 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.58.123501
published as Phys.Rev. D58 (1998) 123501 · AMSTeX, 7 pages, re-submitted to Phys Rev Lett
arxiv created 1998/07/20 · openalex publication_date 1998/11/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the stability of cosmological scaling solutions within the class of spatially homogeneous cosmological models with a perfect fluid subject to the equation of state p_\ensuremathγ=(\ensuremathγ\ensuremath-1)\ensuremathρ_\ensuremathγ (where \ensuremathγ is a constant satisfying 0<\ensuremathγ<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 physical interest. For example, in these models a significant fraction of the current energy density of the Universe may be contained in the scalar field whose dynamical effects mimic cold dark matter. It is known that the scaling solutions are late-time attractors (i.e., stable) in the subclass of flat isotropic models. We find that the scaling solutions are stable (to shear and curvature perturbations) in generic anisotropic Bianchi models when \ensuremathγ<2/3. However, when \ensuremathγ>2/3, and particularly for realistic matter with \ensuremathγ>~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 consequences of these results.