At the end of inflation, the fermionic points
are held apart by degeneracy pressure (no two identical fermions can occupy the
same point). In effect, each fermionic point is vibrating in a little cell
bounded by other fermionic points. The walls of all of the cells are
oscillating in and out as gravity and degeneracy pressure slug it out. This
being a quantum system, the frequency and amplitude of this oscillatory energy
vary from point to point.
If the oscillatory energy at a point is large
enough, it will excite the point, raising it from its ground state energy to
the next energy eigenstate, about twice the ground-state energy. The energy
above the ground state is observed as a particle at that point. Only about 20%
of the oscillatory energy met this requirement in the early universe, so 80% of
it is still there, confounding the physicists desperately trying to find out
what this dark matter is.
Physicists characterize this scenario as
inflaton bosons decaying into standard model particles. The inflaton is the
field that drives inflation and inflaton bosons are fluctuations of that field,
that is, the oscillations. However, these are oscillations of the whole of
spacetime, while particles are excitations of points (or fluctuations of fields
if you prefer).
Theoretical physicists working on dark matter
generally create models in which the dark matter is a particle of some sort.
For example, the model described here correctly assumes that dark matter is the result of incomplete
decay of the inflaton, but then postulates a pair of new fermions, a new field,
and a new symmetry, none of which exists.
Another approach (example here) treats the dark matter halos as Bose-Einstein condensates, agglomerations
of bosons in the same quantum state. If you think of the postinflation
oscillatory energy as inflaton bosons, this approach may seem attractive, but
once again, it assumes these bosons are real particles, while actually they are
oscillations of the mean free path of the fermionic points, that is, they are
oscillations of spacetime itself.
The correct way to think of the dark matter is
not as matter, but as energy stored in spacetime. In the language of general
relativity, this looks like spacetime curvature. It is said that “Matter tells
spacetime how to curve, and spacetime tells matter how to move.” But dark
matter is spacetime curvature without
matter!
In 2010 a group of researchers (see here) examined this possibility and
concluded that a curved region of empty spacetime would look and act exactly like
dark matter! Unfortunately, they felt that this idea was too bizarre to be
realistic and as far as I know they never pursued it. At the time, I e-mailed
the lead author to point out that their idea fit perfectly with the incomplete
decay scenario, but of course, never received a reply.
