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.