J ul 1 99 5 COSMOLOGICAL RESTRICTIONS ON CONFORMALLY INVARIANT SU ( 5 ) GUT MODELS

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) × 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.