68
Topological defects
•
11
~
z
~
.
-11
Figure 3.2. Kink soli ton solution .
•
____ 1) __
,u
Z
<
•
- - - - - - - - - - - - - - - - - + - - - - - - - - - - - - - - - - - - - - - - - --=_:":_=-=_"::_"' -:-,,-------11
Figure 3.3. Antikink soliton solution.
which is broken by the vacuum expectation value of t/). The domain walls connect
the two distinct minima which constitute the complete space of minima. There is
no way to continuously defonn a domain wall to a new object that does not have
its ends at distinct minima. while keeping the energy density finite.
The fonnation of such topological defects can be understood in tenns of
the Kibble mechanism [I], which we now describe. As discussed in chapter 2,
symmetries are expected to be restored at high temperatures. As the universe
cools, it passes through a phase transition and different regions of the universe
undergo phase transitions to different minima of the zero-temperature effective
potential. There will be some correlation length ~ such that the VEVs for points
of space separated by more than about ~ are uncorrelated. The length ~ cannot
be larger than the particle horizon since no influence can have propagated over a
distance greater than this from the big bang to the time of the phase transition.
Topological defects
•
11
~
z
~
.
-11
Figure 3.2. Kink soli ton solution .
•
____ 1) __
,u
Z
<
•
- - - - - - - - - - - - - - - - - + - - - - - - - - - - - - - - - - - - - - - - - --=_:":_=-=_"::_"' -:-,,-------11
Figure 3.3. Antikink soliton solution.
which is broken by the vacuum expectation value of t/). The domain walls connect
the two distinct minima which constitute the complete space of minima. There is
no way to continuously defonn a domain wall to a new object that does not have
its ends at distinct minima. while keeping the energy density finite.
The fonnation of such topological defects can be understood in tenns of
the Kibble mechanism [I], which we now describe. As discussed in chapter 2,
symmetries are expected to be restored at high temperatures. As the universe
cools, it passes through a phase transition and different regions of the universe
undergo phase transitions to different minima of the zero-temperature effective
potential. There will be some correlation length ~ such that the VEVs for points
of space separated by more than about ~ are uncorrelated. The length ~ cannot
be larger than the particle horizon since no influence can have propagated over a
distance greater than this from the big bang to the time of the phase transition.