I. Introduction

It appears very likely that the basic Lagrangian for weak interactions is invariant under a local gauge symmetry (see, e.g., Taylor 1976). However, the observation of masses for bosons and fermions participating in weak interactions shows that such a symmetry is not manifest, at least under the conditions of present experiments. In models for weak interactions, the breaking of the symmetry is usually achieved by the Higgs mechanism. According to this, all massive particles are coupled to a scalar (Higgs) field whose self-couplings are such that it attains a suitable nonzero expectation value in the ''vacuum'' (lowest energy) state. However, there is thus far no direct experimental evidence for or against the existence of Higgs scalar fields (Gaillard 1978). Certainly most of the predictions of models for weak interactions of relevance at presently accessible energies are entirely independent of the mechanism of mass generation. There exist some requirements on the spectrum of masses necessary to maintain the self-consistency of the models (Dicus and Mathur 1973; Lee, Quigg, and Thacker 1977; Politzer and Wolfram 1979; Huang 1979), but none are amenable to immediate experimental investigation. Of course, the observation of a Higgs particle would confirm that the Higgs mechanism is operative, but the prospects for such an observation are probably somewhat remote (Gaillard 1978). In the attempt to investigate the Higgs mechanism one is therefore led to consider its effects in cosmology. The existence of a vacuum expectation value for the Higgs field apparently leads to a very large energy density in the universe (Linde 1974), whose presence is completely contradicted by observation (Weinberg 1972; Misner, Thorne, and Wheeler 1973). However, the introduction of a compensating cosmological constant term into Einstein's equations can be arranged to remove this contradiction (Linde 1974) by providing an effective vacuum energy density which cancels the large vacuum energy density associated with the Higgs field. However, such a cancellation may not have been maintained throughout the evolution of the universe.

There are indications that, at the high temperatures of the early universe, symmetries which are presently ''spontaneously broken'' by the Higgs mechanism should have been restored and that the vacuum expectation value of the Higgs field should then vanish (Kirzhnits and Linde 1972; Kirzhnits 1972). In that case, the large energy density contributed by the Higgs field should have disappeared, leaving uncanceled the cosmological term which must be arranged to remove its effects at lower temperatures. In this paper, we report on the consequences of this phenomenon for the development of the early universe. We find (despite previous claims to the contrary [Bludman and Ruderman 1977]) that it can determine the expansion rate of the universe for a short period, but fortunately this probably does not result in sufficient modification of the evolution of the universe to lead to presently observable effects.

This paper is organized as follows. In S III we discuss the gravitational effects of a Higgs condensate (Higgs field with a classical vacuum expectation value). In S II we consider the restoration of spontaneously broken symmetries in the early universe and its consequences for the evolution of the universe.

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