Cosmological Restrictions on Conformally Invariant SU(5) GUT Models

TL;DR

This paper applies Dirac's constrained Hamiltonian formalism to a conformally invariant SU(5) GUT model in a de Sitter universe, deriving constraints that restrict the residual gauge symmetry and confirming a prolonged inflationary phase.

Contribution

It demonstrates the presence of second-class constraints in the SU(5) GUT model and shows how they restrict the gauge symmetry during the early universe's de Sitter phase.

Findings

Residual gauge symmetry is limited to SU(3) x SU(2) x U(1) during inflation

Numerical solutions confirm a long de Sitter phase consistent with cosmological models

Second-class constraints are crucial for understanding gauge symmetry in early universe

Abstract

Dirac's theory of constrained Hamiltonian systems is applied to the minimal conformally invariant SU(5) grand-unified model studied at 1-loop level in a de Sitter universe. For this model, which represents a simple and interesting example of GUT theory and at the same time is a step towards theories with larger gauge group like SO(10), second-class constraints in the Euclidean-time regime exist. In particular, they enable one to prove that, to be consistent with the experimentally established electroweak standard model and with inflationary cosmology, the residual gauge-symmetry group of the early universe, during the whole de Sitter era, is bound to be SU(3) x SU(2) x U(1). Moreover, the numerical solution of the field equations subject to second-class constraints is obtained. This confirms the existence of a sufficiently long de Sitter phase of the early universe, in agreement with the initial assumptions.