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at all times, while the non-tilded parameters satisfy it only at the present time.  We are now able to obtain the full system of equations the govern the background expansion in this model:  \begin{equation}  \end{equation} \begin{eqnarray}  E^2(z) = g(z)[\Omega_m(z) + \Omega_\Lambda(z)],\\  (\Omega_m + \Omega_\Lambda) dg + g d \Omega_\Lambda = 0, \\  \Omega_\Lambda(z) = \Omega_\Lambda^0 + \nu [E^2(z) - 1], \\  \Omega_m(z) = \Omega_m^0 (1+z)^{3(1+w_n)},  \end{eqnarray}