On a cosmological aspect of the phase transition at the grand unification temperature

Abstract

The phase transition at the temperature of grand unification is studied in the curved space-time of a Friedmann universe, using the minimal SU(5) model of Georgi and Glashow. As a result of the changes induced in the scalar field ϕ by the cosmological expansion, a kinetic energy term appears in the phase with broken symmetry, for which 〈0|ϕ|0〉 is non-zero. An estimate of the importance of this hitherto neglected cosmological kinetic term is obtained by calculation from the flat-space solution elaborated by Daniel and Vayonakis. When there is very little supercooling, and for certain values of the constants in the theory, and if the X-boson mass m X is of order 3 × 10 15 GeV, then this kinetic energy has about the same magnitude as the effective potential at the temperature T 1, corresponding to the limit of metastability of the symmetric phase. At higher temperatures and for higher values of m X, the kinetic energy can be dominant. At lower temperatures, and when there is much supercooling, then it is negligible. The significance of this result is discussed, including its consequences for theories, such as have sometimes been proposed, which demand a high value for m X, and for the “superconducting” universe of Mohapatra and Senjanović. The mechanism for the suppression of the production of magnetic monopoles suggested by Bais and Rudaz is re-examined. Their key assumption that the phase transition is only weakly of first order is shown not to hold for the range of parameters which they use. But the contention of Linde that the transition is always strongly of first order is also found not to be true. The theory can be designed so that the phase transition is weakly of first order. Then, the effect of the kinetic energy may be significant, but will not be large enough to make the model of Bais and Rudaz viable.