Gravitational frameworks and the dynamics of scaler fields

Scalar fields describe interesting phenomena such as Higgs bosons, dark matter and dark energy, and is found to be quite common in physical theories. These fields are susceptible to gravitational forces so that being massless is not enough to remain conformal invariant. They should also be connected directly to the scalar curvature. Because of these characteristics, in this thesis we investigated the structure and interactions of scalar fields under the conformal transformations. We show how to reduce the quadratic quantum contributions in the single scalar field theory. On the other hand, for the multi-scalar field theories, we analyzed the interactions in certain limits. This thesis suggests a new method for stabilizing Higgs bosons.