{2a^4}}-{Mk\over 2}+3a^2V(\phi)]\\
{\partial P_\phi}\over {\partial t}&=&-a^3{{\partial V}\over{\partial \phi}}\end{aligned}$$ The above four equations along with the Hamiltonian constraint (8) determine t and also the paths characterized by $a$. Our aim is to find the extrema of the action when $ a,t~~  and~~  \phi $ are complex i.e., we are looking at complex four-metrics and complex fields on a real four dimensional manifold characterized by the coordinates $ t, r, \theta , \phi $. To fix the origin of time defined above and to impose regularity condition on the four geometry at $ a=0 $, we choose the boundary condition as [@unru:gr-qc] $$a(t=0)=0,~~ {{\partial a}\over{ \partial t}}= \beta ~i~ at~ t=0,$$ where $\beta=\pm 1$. For analytical simplicity we also assume that $V(\phi)$ is approximately constant, near about the region where (15) is satisfied. We find using (12) and (14) $$a^3 {{\partial \phi}\over {\partial t}}= constant.$$ If this constant is non-zero the boundary condition at $ t=0 $ leads $ {{\partial \phi}\over {\partial t}}\rightarrow \infty $. Hence we should have $ \phi=constant $. This implies $ P_\phi=0 $. Under this condition, when $V(\phi)\simeq V_0 $ the solutions of (11)- (14) are called the zeroth order solutions. We write $$P_a\approx {P_a}^0={{\partial S_0}\over {\partial a}}$$ 