where the coupling constants have their renormalized values. $S_{g_+}$ represents the classical gravitational part of the action. $M^{{\pm}^2} = {\tilde{m}}^{{\pm}^2} + \ha \l {\mbox{$\chi_{0}$}}^{{\pm}^2} $, and ${ K}$ and ${\bar{K}}$ are complex nonlocal kernels with explicitly known forms. The effective equations of motion are obtained from this effective action via [^5]

\_ = 0 \_ = 0

Since we are interested in comparing with (2.13) which is equivalent to the $G_{00}$ Einstein equation with backreaction, we need the first integral form of (2.16), which can be derived as & & [12]{}[a’]{}\^2 - [12]{}’\^2 + [12]{} m\^2 a\^2 \^2 - [12]{} a\^2 + [ł4!]{}\^4 -[13ł96]{}\^2 - [1348]{}m\^2 a\^2 - [116]{} M\^2 ln a\
& & + [132]{}d\_1 M\^2()[K]{}(- \_1)M\^2(\_1) = 0 with the assumption of having no quanta of the higher modes in the initial state. ${\cal K} = K + \bar{K}$ and is real and hence the above equation is also manifestly real. Equation (2.17) is then equivalent to the effective $G_{00}$ Einstein equation or the Einstein- Hamilton- Jacobi equation plus backreaction. This in turn can be identified with (2.13), the effective Wheeler- De Witt equation in the WKB limit. Therefore, comparing (2.17) and (2.13) we can identify the backreaction 