Model Independent Accelerating Universe and the Cosmological Coinc idence Problem

We show that the evolution of the quintessence energy density $\Omega_Q$ is model independent in an accelerating universe. The accelerating behaviour has lasted at most 0.5 e-folds of expansion assuming a present day value of $\Omega_Q=2/3$. The generic evolution differs from the exact solution by a percentage given by $r=2\gm_Q$, with $\gm_Q=(\rho_Q+p_Q)/\rho_Q$. For a small $\gm_Q$ the evolution remains a good approximation for a long period. Nucleosynthesis bounds on $\Omega_Q$ 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 $a_i \ll a_o$. Finally, we discuss the relevance of this result to the cosmological coincidence problem.