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The functional formulation and one-loop effective action for scalarself-interacting theory non-linearly coupled with some power of the curvatureare studied. After the explicit one-loop renormalization at weak curvature, weinvestigated numerically the phase structure for such unusual phi^4 theory. Itis demonstrated the possibility of curvature-induced phase transitions forpositive values of the curvature power, while for negative values the radiativesymmetry breaking does not take place. The dynamical mechanism for theexplanation of the current smallness of the cosmological constant is presentedfor several models from the class of theories under consideration.Comment: 25 pages, 20 eps figures, use iopart.cls; minor corrections,  references added, to appear in JCA

journal of cosmology and astroparticle physics

The one-loop effective action in phi<sup>4</sup>theory coupled non-linearly with the power of the curvature and the dynamical origin of the cosmological constant

The one-loop effective action in phi4theory coupled non-linearly with the power of the curvature and the dynamical origin of the cosmological constant

The one-loop effective action in phi⁴theory coupled non-linearly with the power of the curvature and the dynamical origin of the cosmological constant