One-loop effective potential for λφ4 theory in de Sitter space

We calculate, by summing the eigenvalues, and numerically evaluate the one-loop effective potential for the single real scalar theory in de Sitter space. The result is compared with that obtained in the normal-coordinate expansion. The comparison indicates an implausibility of the approximation based on the normal-coordinate expansion at the point where the effective mass vanishes. We also show that the normal-coordinate expansion becomes a poor approximation for large curvature. (orig.)