Singularities in Einstein-conformally coupled Higgs cosmological models

TL;DR

This paper analyzes the behavior of Einstein-conformally coupled Higgs fields near initial singularities, classifying different types of singularities and revealing a new 'Small Bang' singularity where the Higgs field remains bounded.

Contribution

It provides an analytical and numerical classification of singular solutions in Einstein-conformally coupled Higgs cosmologies, introducing a new 'Small Bang' singularity type.

Findings

Identified three types of singular solutions: 'Small Bang', Milne type, and 'Big Bang'.

Discovered a new 'Small Bang' singularity with bounded Higgs field and curvature.

Showed that near singularities, the Higgs sector lacks symmetry breaking vacuum states.

Abstract

The dynamics of Einstein-conformally coupled Higgs field (EccH) system is investigated near the initial singularities in the presence of Friedman-Robertson--Walker symmetries. We solve the field equations asymptotically up to fourth order near the singularities analytically, and determine the solutions numerically as well. We found all the asymptotic, power series singular solutions, which are (1) solutions with a scalar polynomial curvature singularity but the Higgs field is bounded (`Small Bang'), or (2) solutions with a Milne type singularity with bounded spacetime curvature and Higgs field, or (3) solutions with a scalar polynomial curvature singularity and diverging Higgs field (`Big Bang'). Thus, in the present EccH model there is a new kind of physical spacetime singularity (`Small Bang'). We also show that, in a neighbourhood of the singularity in these solutions, the Higgs sector does not have any symmetry breaking instantaneous vacuum state, and hence then the Brout-Englert-Higgs mechanism does not work. The large scale behaviour of the solutions is investigated numerically as well. In particular, the numerical calculations indicate that there are singular solutions that cannot be approximated by power series.