Abstract
I will talk about the production of magnetic monopoles in the early Universe. Because of time limitations, my talk will not be self-contained. The general properties of magnetic monopoles have been reviewed at this conference by D. Olive1, and a generalization of the Bogomolny lower bound on their masses has been discussed by D. Scott2.
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References
D. Olive, these proceedings p. 451.
D.M. Scott, DAMTP Cambridge preprint 80–2 (1980).
See, e.g., S. Coleman, “Classical Lumps and Their Quantum Descendants”, in new Phenomena in Subnuclear Physics, ed. A. Zichichi, ( Plenum Press, N.Y., 1977 ).
A review of spontaneous symmetry breakdown in finite temperature field theory may be found in A.D. Linde, Rep. Prog, in Phys. 42 (I) (1979) 389.
V.L. Ginzburg, Yad. Fiz. 2 (I960) 2031[Sov. Phys. Solid State 2 (1960) 1824].
It is not necessary that the pattern precisely follow Eq. (1).
This argument has been applied in the present context by T.W.B. Kibble, J. Phys. A: Math. Gen. 9 (1976) 1387.
D.A. Kirzhnits and A.D. Linde, Ann. Phys. 101 (1976) 195.
It is important to recall also that if the Higgs mass is too small, radiative corrections restore the symmetry even at zero temperature. For the Abelian Higgs model (Ref. 8), it is necessary that m 2H > (3/2)α m 2X .
J. Ellis, M.K. Gaillard and D.V. Nanopoulos, these proceedings p. 461.
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M.B. Einhorn, D. Stein and D. Toussaint, Phys. Rev. D, to be published.
The determination of d is a problem to which we will return shortly.
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Here we are assuming a radiation-dominated epoch and neglecting any cosmological constant. For the second-order phase transition, this is a good approximation. See Linde, Ref. 4, and S. A. Bludman and M.A. Ruderman, Phys. Rev. Letters 18 (1977) 255.
G. Steigman (private comnunication) suggests that the upper limit of 10-19 might well be improvable to 10-25, in which case stable monopoles could not have been produced above 1010 GeV.
This inference seems more general than the Abelian Higgs model. See S. Weinberg, Phys. Rev. D9 (1974) 3357.
The suggestion of a first-order phase transition was given in Ref. 13 and also, independently, by A.H. Guth and S.-H.H.Tye, Phys. Rev. Letters 44 (1980) 631, in which the process is described in some detail. The analysis presented here does not agree in some respects with that given by Guth and Tye. In particular, their neglect of the cosmological constant and their approximation of the thermal nucleation rate are questionable.
A.D. Linde, Phys. Letters 70B (1977) 306 and Ref. 4.
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These considerations were also described by Guth and Tye, op. cit.
If one is considering a GUT like SU(5), other unnatural adjustments are made in the Higgs potential anyway.
K. Sato, “First Order Phase Transition of a Vacuum and Expansion of the Universe”, NORDITA preprint, January 1980.
This is apt to be a much better approximation than the step function assumed by Guth and Tye, op.cit.
This and other aspects of the implications of a first-order phase transition on the monopole problem are under consideration by Sato and myself.
S. Weinberg, “The Problem of Mass”, in Transactions of the New York Academy of Sciences, Series II, Vol. 38 (1977) 185.
G.’t Hooft, Cargese Sumner Lecture III (1979).
S. Dimopoulos and L. Susskind, Nucl. Phys. B155 (1979) 237.
E. Eichten and K. Lane Phys. Letters 90B (1980) 125.
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Einhorn, M.B. (1980). The Production of Magnetic Monopoles in the Very Early Universe. In: Ferrara, S., Ellis, J., van Nieuwenhuizen, P. (eds) Unification of the Fundamental Particle Interactions. Ettore Majorana International Science Series, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3171-1_31
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