Abstract
We show that the evolution of the quintessence energy density ΩQ is model independent in an accelerating universe. The accelerating behavior has lasted at most 0.5 e-folds of expansion assuming a present day value of ΩQ=2/3. The generic evolution differs from the exact solution by a percentage given by r=2γQ, with γQ=(ρQ+pQ)/ρQ. For a small γQ the evolution remains a good approximation for a long period. Nucleosynthesis bounds on ΩQ suggest that the model independent solution is valid for at least 12 e-folds of expansion which includes then the scale of radiation and matter equality. We can, therefore, establish model independent conditions on the cosmological parameters at some factor scale ai≪a0. Finally, we discuss the relevance of this result to the cosmological coincidence problem.
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