Cosmological restrictions on conformally invariant SU(5) GUT models

Abstract

Dirac's (1964) theory of constrained Hamiltonian systems is applied to the minimal conformally invariant SU(5) grand-unified model studied at one-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)*SU(2)*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.