Spontaneously Broken SU(5) Symmetries and One-Loop Effects in the Early Universe

TL;DR

This paper investigates the effects of curvature on the one-loop effective potential and spontaneous symmetry breaking patterns of SU(5) gauge theory in de Sitter space, providing detailed algebraic and numerical analysis of stability and symmetry breaking.

Contribution

It generalizes an algebraic technique to analyze spontaneous symmetry breaking of SU(5) in de Sitter space, including cubic terms in the potential, and clarifies the stability of various subgroup extrema.

Findings

Stability of extrema in maximal subgroups identified.

Predicted inflationary universe slide into specific symmetry-breaking minima.

Method allows easy generalization to more complete SU(5) potentials.

Abstract

This paper studies one-loop effective potential and spontaneous-symmetry-breaking pattern for SU(5) gauge theory in de Sitter space-time. Curvature effects modify the flat-space effective potential by means of a very complicated special function previously derived in the literature. An algebraic technique already developed by the first author to study spontaneous symmetry breaking of SU(n) for renormalizable polynomial potentials is here generalized, for SU(5), to the much harder case of a de Sitter background. A detailed algebraic and numerical analysis provides a better derivation of the stability of the extrema in the maximal subgroups SU(4) x U(1), SU(3) x SU(2) x U(1), SU(3) x U(1) x U(1) x R(311), SU(2) x SU(2) x U(1) x U(1) x R(2211), where R(311) and R(2211) discrete symmetries select particular directions in the corresponding two-dimensional strata. One thus obtains a deeper understanding of the result, previously found with a different numerical analysis, predicting the slide of the inflationary universe into either the SU(3) x SU(2) x U(1) or SU(4) x U(1) extremum. Interestingly, using this approach, one can easily generalize all previous results to a more complete SU(5) tree-level potential also containing cubic terms.