I. Introduction

The simplest grand unified gauge model is based on the gauge group SU(5), and contains Higgs bosons in the and representations.[1] To avoid inconsistency with the measured light-fermion-mass spectrum,[2] and to allow generation of the observed cosmological baryon asymmetry in the early universe, [3,4] this minimal model must be supplemented by an additional or Higgs-boson representation. The resulting model involves at least 100 particle degrees of freedom. Low-energy phenomenology potentially provides a few indications that this model should be extended. Avoidance of instanton-induced violation in QCD without necessity for an observable axion suggests doubling the Higgs multiplet, and requires an additional Higgs multiplet.[5] Observation of small neutrino masses or oscillations would support models based on the gauge group SO(10).[6] Explanations of results from present or anticipated experiments do not appear to require models more complicated than these. However, explicit implementations of several general theoretical schemes do appear to involve significantly more complicated models, containing many more particle degrees of freedom. Supersymmetric models suggest at least a doubling in the number of fundamental fields, and often require additional fields to obtain the required pattern of symmetry breaking.[7] Models with ``hypercolor'' require large numbers of particles to arrange for appropriate mixings and mass spectra.[8] For example, the SO(10)[5] model of Ref. [9] involves at least 225 gauge bosons, 305 fermions, and 11485 Higgs bosons, giving a total of 12015 fundamental fields. Models with subquark structure imply many effectively point-like particles, including radial and orbital excitations. Models based on reduction from above four dimensions yield an infinite sequence of ``particle'' states corresponding to quantized excitations in the compactified dimensions.[10]

Low-energy phenomena are for the most part unaffected by the presence of large numbers of very heavy particles. Only in the early universe are sufficient energies available such that the presence of heavy particles may be significant. The purpose of this paper is to consider the consequences of very complicated gauge models for the evolution of the early universe, and to use existing cosmological observations to infer constraints on the particle content of these models. In most cases, the overall structure of complicated models is defined by general theoretical principles, but details such as values of Higgs-boson couplings and other parameters are left undetermined. We attempt, therefore, to obtain results which depend only on gross properties of models, and are insensitive to their details. In some cases, we resort to a statistical analysis, and extract general features from averages over statistical ensembles of models with distributions of values for undetermined parameters.

This paper assumes the standard ``hot big bang'' model for the early universe. Most of its results nevertheless also apply in the ``hot'' phases of ``inflationary'' models.

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