Quantum Cosmology and Grand Unification

Quantum cosmology may restrict the class of gauge models which unify electroweak and strong interactions. In particular, if one studies the normalizability criterion for the one-loop wave function of the universe in a de Sitter background one finds that the interaction of inflaton and matter fields, jointly with the request of normalizability at one-loop order, picks out non-supersymmetric versions of unified gauge models. The investigations in modern cosmology have been devoted to two main issues. On one hand, there were the attempts to build a quantum theory of the universe with a corresponding definition and interpretation of its wave function [1,2]. On the other hand, the drawbacks of the cosmological standard model motivated the introduction of inflationary scenarios. These rely on the existence of one or more scalar fields, and a natural framework for the consideration of such fields is provided by the current unified models of fundamental interactions (see, for example, Ref. [3] and references therein). The unification program started with the proposal and the consequent experimental verification of the electroweak standard model (SU(3)C ⊗ SU(2)L ⊗ U(1)Y ), and has been extended to other simple gauge groups, like SU(5), SO(10) and E6. All of them in fact, even if with different capability, unlike the electroweak standard model are able to allocate all matter fields in a few irreducible representations (IRR) of the gauge group, and require a small number of free parameters. However, since these enlarged gauge models predict new physics, a first source of constraints upon them is certainly provided by the experimental bounds on processes like proton decay, neutrino oscillations, etc. [4]. Further restrictions can be obtained from their cosmological applications, as discussed in Ref. [5].