The One-Loop Effective Action in phi^4 Theory Coupled Non-Linearly with Curvature Power and Dynamical Origin of Cosmological Constant

TL;DR

This paper develops the one-loop effective action for a scalar phi^4 theory with non-linear curvature coupling, revealing curvature-induced phase transitions and proposing a dynamical explanation for the small cosmological constant.

Contribution

It introduces a novel analysis of scalar field theories with non-linear curvature coupling, including explicit renormalization and phase structure investigation.

Findings

Curvature-induced phase transitions occur for positive curvature power.

Radiative symmetry breaking is absent for negative curvature power.

A dynamical mechanism explains the smallness of the cosmological constant.

Abstract

The functional formulation and one-loop effective action for scalar self-interacting theory non-linearly coupled with some power of the curvature are studied. After the explicit one-loop renormalization at weak curvature, we investigated numerically the phase structure for such unusual phi^4 theory. It is demonstrated the possibility of curvature-induced phase transitions for positive values of the curvature power, while for negative values the radiative symmetry breaking does not take place. The dynamical mechanism for the explanation of the current smallness of the cosmological constant is presented for several models from the class of theories under consideration.