**5.3. Unwanted Relics**

We have spoken in the last lecture about grand unified theories (GUTs),
and also about topological defects. If grand unification occurs
with a simple gauge group *G*, any spontaneous breaking of *G*
satisfies
_{2}(*G* /
*H*) = _{1}(*H*)
for any simple subgroup *H*. In particular,
breaking down to the standard model will lead to magnetic monopoles, since

(186) |

(The gauge group of the standard model is, strictly speaking,
[*SU*(3) × *SU*(2) × *U*(1)] /
_{6}. The
_{6} factor, with
which you may not be familiar, only affects the
global structure of the group and not the Lie algebra, and thus
is usually ignored by particle physicists.)

Using the Kibble mechanism, the expected relic abundance of monopoles works out to be

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This is far too big; the monopole abundance in GUTs is a serious problem for cosmology if GUTs have anything to do with reality.

In addition to monopoles, there may be other model-dependent relics predicted by your favorite theory. If these are incompatible with current limits, it is necessary to find some way to dilute their density in the early universe