Dynamical system analysis at background and perturbation levels: Quintessence in severe disadvantage comparing to ΛCDM

We perform for the first time a dynamical system analysis of both the background and perturbation equations, of Lambda CDM cosmology, and quintessence scenario with an exponential potential. In the former case the perturbations do not change the stability of the late-time attractor of the background equations, and the system still results in the dark-energy-dominated, de Sitter solution, having passed from the correct dark-matter era with gamma approximate to 6/11. However, in the case of quintessence the incorporation of perturbations changes the stability and properties of the background evolution, and the only conditionally stable points present an exponentially increasing matter clustering, not favored by observation; thus, this situation is not physically interesting. This result is a severe disadvantage of quintessence cosmology compared to the Lambda CDM paradigm.