Abstract
The 1-loop renormalized effective potential for a phi 4 theory in the early Universe with a small inhomogeneity is evaluated under the adiabatic approximation. It is used to investigate the Coleman-Weinberg symmetry breaking processes usually leading to inflationary cosmologies in the presence of an inhomogeneity. The result shows that whether the symmetry is radiatively broken or not will crucially depend upon the scalar-gravitational coupling xi and the magnitude of the scalar curvature R. In particular, the author shows how the mode-mixing behaviour resulting from the inhomogeneity of spacetime is naturally replaced by introducing the non-local term into the field equation. This property allows the analysis of other quantum field effects in the inhomogenous spacetime, which will be presented in later papers.
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