176 Inflationary cosmology and creation of matter in the universe
Figure 4.3.Broad parametric resonance for the fieldχin Minkowski space in the theory
1
2 m
(^2) φ (^2). For each oscillation of the fieldφ(t)the fieldχkoscillates many times. Each peak
in the amplitude of the oscillations of the fieldχcorresponds to a place whereφ(t)=0.
At this time the occupation numbernkis not well defined, but soon after that time it
stabilizes at a new, higher level, and remains constant until the next jump. A comparison
of the two parts of this figure demonstrates the importance of using proper variables for the
description of pre-heating. Bothχkand the integrated dispersion〈χ^2 〉behave erratically
in the process of parametric resonance. Meanwhilenkis an adiabatic invariant. Therefore,
the behaviour ofnkis relatively simple and predictable everywhere except at the short
intervals of time whenφ(t)is very small and the particle production occurs.
Expansion of the universe modifies this picture for many reasons. First of all,
expansion of the universe’s redshifts produced particles, making their momenta
smaller. More importantly, the amplitude of oscillations of the fieldφdecreases
because of the expansion. Therefore the frequency of oscillations of the fieldχ
also decreases. This may destroy the parametric resonance because it changes,
in an unpredictable way, the phase of the oscillations of the fieldχeach moment
thatφbecomes close to zero.
That is why the number of created particlesχmay either increase or decrease
each time when the fieldφbecomes zero. However, a more detailed investigation