148 Cosmological models
from an essentially homogeneous early state (via amplification of initial quantum
fluctuations)—a major success if the all the details can be sorted out.
This is an attractive scenario, particularly because it ties in the large-scale
structure of the universe with high-energy physics. It works fine for those regions
that start off close enough to FL models, and, as noted earlier this suffices to
explain the existence of large FL-like domains, such as the one we inhabit. It does
not necessarily rule out the early and late anisotropic modes that were discussed
in the section on Bianchi models. It fits the observations provided one has
enough auxiliary functions and parameters available to mediate between the basic
theory and the observations (specifically, evolution functions, a bias parameter
or function, a dark matter component, a cosmological constant or ‘quintessence’
component at late times). However, it is not at present a specific physical model,
rather it is a family of models (see e.g. [78]), with many competing explanations
for the origin of the inflaton, which is not yet identified with any specific matter
component or field. It will become a well-defined physical theory when one or
other of these competing possibilities is identified as the real physical driver of an
inflationary early epoch.
There are three other issues to note here. First, theissue of probability:
inflation is intended as a means of showing the observed region of the universe is
in fact probable. But we have no proper measure of probability on the family
of universe models, so this has not been demonstrated in a convincing way.
Second, theTrans-Planckian problem[96]: inflation is generally very successful
in generating a vast expansion of the universe. The consequence is that the
spacetime region that has been expanded to macroscopic scales today is deep
in the Planck (quantum-gravity) era, so the nature of what is predicted depends
crucially on our assumptions about that era; but we do not know what conditions
were like there, and indeed even lack proper tools to describe that epoch, which
may have been of the nature of a spacetime foam, for example. Thus the results of
inflation for large-scale structure depend on specific assumptions about the nature
of spacetime in the strong quantum gravity regime, and we do not know what
that nature is. Penrose suggests it was very inhomogeneous at that time, in which
case inflation will amplify that inhomogeneous nature rather than creating spatial
homgeneity. As in the previous case, whether or not the process succeeds will
depend on the initial conditions for the expansion of the universe as it emerges
from the Planck (quantum gravity) era. Thirdly, there are still unsolved problems
regardingthe end of inflation. These relate to the fact that if one has a very slow
rolling field as is often claimed, then the inertial mass density is very close to zero
so velocities are unstable.
It must be emphasized that in order to investigate this issue of isotropisation
properly,one must examine the dynamical behaviour of very anisotropic and
inhomogeneous cosmologies. This is seldom done—for example, almost all of
the literature on inflation examines only its effects in RW geometries, which
is precisely when there is no need for inflation take place in order to explain
the smooth geometry—for then a smooth geometry has been assumedapriori.