A magnetic monopole would be a magnet with only one pole. In other words, it would have net magnetic charge. But magnetic monopoles have never been observed or created experimentally. When a magnet with a north and south pole is cut in half, it becomes two magnets, each with its own north and south poles. There doesn’t seem to be a way to create a magnet with only one pole. Yet particle theories like Grand Unified Theories and superstring theory predict magnetic monopoles should exist.
In particle theory, a magnetic monopole arises from a topological glitch in the vacuum configuration of gauge fields in a Grand Unified Theory or other gauge unification scenario. The length scale over which this special vacuum configuration exists is called the correlation length of the system. A correlation length cannot be larger than causality would allow, therefore the correlation length for making magnetic monopoles must be at least as big as the horizon size determined by metric of the expanding Universe.
According to that logic, there should be at least one magnetic monopole per horizon volume as it was when the symmetry breaking took place.
This creates a problem, because it predicts that the monopole density today should be 1011 times the critical density of our Universe, according to the Big Bang model.
But so far, physicists have been unable to find even one.
How Inflation Solves It
Monopoles are still created in inflationary models. They’re just created before (or during) inflation, so that the rapid expansion thereafter dilutes their density to unobservably low levels.
At the time when the monopoles are created, they’re created at a density of order 1 per Hubble volume — that is, there’s one in each “observable Universe” at that time. In general, when a symmetry breaks, topological defects form that are separated on a length scale of order (speed of propagation of the field)(time scale over which the symmetry breaks). The first is of order, and the second is of order the Hubble time, so monopoles are separated by a distance of order the Hubble length.
You should take “of order” here very liberally — I don’t actually care if I’m off by factors ofor or anything measly like that! After all, inflation blows up lengths by something like or more. So one monopole per horizon volume becomes one per horizon volumes. (Also, the horizon volume continues to change after inflation is over, but not by anything like this sort of factor.)
With densities like that, we certainly wouldn’t expect to see any monopoles. Problem solved