Monopoles-Breakdown of Symmetry

Inflation for Astronomers: "MONOPOLES The spontaneous breakdown of symmetry in the GUT scenario causes the initial larger symmetry group of the unified interactions to decompose into smaller ones, which include the symmetry group of the electromagnetic theory. A general theorem tells us that whatever the initial symmetry group, the process of symmetry breaking inevitably generates physical solutions that describe magnetic monopoles. The energy of a monopole is about 1016 GeV, corresponding to a mass of about 1.8 x 10-8 g. Assuming that no more than one monopole is created in one horizon-size sphere, the mass density of monopoles at the GUTs epoch works out to about 1.7 x 1065 gcm-3.This is diluted by expansion through a factor of about 4 x 1026 to a present mass density of 10-15 g cm-3 - far in excess of the critical density. With a density of this order, the universe would have contracted to a = 0 in time less than 105 years! Since monopoles are stable objects, they cannot be destroyed. Thus the problem of excess monopole density seems insurmountable within the standard model."
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DOMAIN WALLS
The GUTs phase transition produces certain characteristic discontinuities in the matter distribution. This happens during the spontaneous breakdown of symmetry, which leads the mediating scalar fields to have a discrete set of characteristic values. Thus one region or ``domain'' has one value of the scalar field, while its neighbor has another. The boundary wall between the domains would therefore be a region of discontinuity. We expect to see this as a sheet of inhomogeneity in the large scale matter distribution in the universe. The present data do not reveal any such inhomogeneity in the observable universe.
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SMOOTHNESS PROBLEM
The horizon problem discussed above was in the context of the large-scale homogeneity in the universe. A related problem arises when we take into account the extraordinary smoothness of the MBR at small angles (for a review see 32, 96, 128). The difficulty for the standard model comes from the chronology of the proposed scenario in which discrete structures are supposed to evolve from primordial seeds. Most theories of structure formation predict that some imprint of this event remains on the MBR in the form of small fluctuations of the order T / T ~ 10-4 in the temperature over angular sizes ranging from a few arc seconds to a few arc minutes. Contrary to these expectations no such fluctuations have been detected. The current upper bounds are T / T 10-5. We discuss this point at length in Section 2.3.
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THE λ-TERM The cosmological constant was introduced by Einstein somewhat empirically to arrive at a static model of the universe (38). Although with the discovery of the cosmological redshift law by Hubble, the original need for disappeared, it is still taken seriously by many cosmologists. Observationally, the value of has to be of the order of the square of Hubble's constant at present. Thus | | 10-35 s-2.

The GUTs epoch generates a cosmological term purely from quantum field theoretical effects. The order of magnitude of this term is very large, however, about ~ 1070 s-2. Thus we have to find why the present -term is smaller by an order ~ 10-105 of the primordial -term.
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