5.7.2. Multi-field theories
A recent trend in inflationary model building has been the exploration of
models with more than one scalar field. The classic example is the hybrid
inflation model,
[13]
which seems particularly promising for
particle physics model building. The simplest version has a potential
with two fields 
and
of the form
which is illustrated in Figure 4. When
Figure 4. The potential for the hybrid
inflation model. The field rolls down the channel at
While in the `channel', which is where all the interesting behaviour takes
place, this is just like a single field model with an effective potential
for
This is a fairly standard form, the unusual thing being the constant term,
which would not normally be allowed as it would give a present-day
cosmological constant. The most interesting regime is where that constant
dominates, and it gives quite an unusual phenomenology. In particular, the
energy density during inflation can be much lower than normal while still
giving suitably large density perturbations, and secondly the field
Within the more general class of two and multi-field inflation models,
it is quite common for only one field to be dynamically important, as
in the hybrid inflation model - this effectively reduces the
situation back to the single field case of the previous subsection.
However, it may also be possible to have more than one important
dynamical degree of freedom. In that case there is no attractor
behaviour giving a unique route into the potential minimum, as in the
single field case; for example, if the potential is of the form of an
asymmetric bowl one could roll into the base down any direction. In
that situation, the model loses some of its predictive power, because
the late-time behaviour is not independent of the initial
conditions. (5)
5 Of course, there is no requirement that
the `true' physical theory does have predictive power, but it would be
unfortunate for us if it does not.
2 is large,
the
minimum of the potential in the -direction
is at = 0. The field rolls down this
`channel' until it reaches
inst2 =
M2 /
', at
which point = 0 becomes unstable
and the field rolls into one of the
true minima at = 0 and
= ±M.
= 0 until it
reaches the critical value, then
falls off the side to the true
minimum at = 0 and
= ±M.
of the form
can be rolling extremely slowly which is of benefit to particle physics
model building.