Spontaneously broken symmetries in gravitational fields (Q1067633)

Models of spontaneous symmetry breakdown by scalar fields in curved space-time are the subject of this concise article reviewing a substantial amount of published work. Model systems consisting of classical gravity (curved space-time) and nongravitational quantum fields are assumed to be self-consistent. The primary object of interest is the gravitational field, which must satisfy constraint and (anomalous) field equation. Gravity is treated initially as a gaugelike field (Lagrangian quadratic in the curvature tensor and its contractions). A quadratic Higgs self-interaction emerges in a natural way from the field equations. The field equations with Robertson-Walker metric are shown to have the nonsingular de Sitter vacuum solution. A model calculation leads to the conformal anomaly. Then Einstein gravity is assumed and further extensive model calculations demonstrate that spontaneous symmetry breakdown may eliminate the cosmological singularity.