Radiative Symmetry Breaking and Dynamical Origin of Cosmological Constant in ${\varphi }^4$ Theory with Non-Linear Curvature Coupling

A scalar self-interacting theory non-linearly coupled with some power of the curvature have a possibility to explain the current smallness of the cosmological constant. Here one concentrate on a massless scalar field in the four-dimensional Fridmann-Robertson-Walker (FRW) spacetime with flat spatial part. One show the phase structure of radiative symmetry breaking and review a dynamical resolution of the cosmological constant problem.