Triviality and renormalization of scalar fields in anisotropic spacetimes

The renormalization and triviality of theory in the Bianchi type I and Kantowski - Sachs type of spacetimes are investigated within the variational Gaussian approach. It is used to see how the space curvature will affect the triviality of the quantum field. For reasons of mathematical technique it is assumed that the spacetimes are slowly varying, and the adiabatic approximation is adopted in the calculations. Our analysis shows that in some situations, which depend upon the metric function, the space anisotropy and magnitude of curvature coupling, Stevenson's precarious phase will disappear and only the trivial phase will remain.