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During inflation, the universe is thought to have cooled by a "factor of 100,000 or so"

The abstract of this paper mentions 'preheating' as playing a role in particle production. Is this 'preheating' referring to inflation?

Because I am trying to communicate this to a non-science audience, I need to use analogies. I previously understood it as reheating 'cooking' the first particles... however, the above seems to suggest that supercooling 'condensed' the first particles, which seems to make more sense. Which of these two analogies is more correct?

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During inflation you have the inflaton field which stays almost constant in a flat region of its potential and therefore drives the exponential expansion of the universe. Because the universe expands by a huge amount during inflation ($\sim e^{60}$) the energy density of any particles that there might have been is diluted and therefore, for all intents and purposes, at the end of inflation the universe is empty of any particles and is only filled with the inflaton field (and possibly with other light scalar fields).

Inflation ends when the inflaton field reaches the end of a flat region of its potential and at this point the inflaton field starts to oscillate around the miminum of its potential. The field can then be interpreted as a condensate of inflaton particles at rest. If the inflaton is coupled to the fields of the Standard Model this condensate will decay into the quanta of these fields. Thus the inflaton field will decay into the particles of the Standard Model which will interact among themselves and thus obtain a thermal distribution (thermalize) leaving a hot soup of particles that serves as the initial state for the conventional Big Bang evolution. This is known as reheating.

Reheating as described above happens perturbatively, that is, in the usual particle physics fashion where one type of particle decays into, say, a pair of another type of particle with the momenta which are half of the rest mass of the initial particle. However, there are other processes which can produce particles from an oscillating inflaton field which are non-perturbative and cannot be described in terms of particles decaying into each other. This non-perturbative production of particles typically happens before the perturbative reheating and therefore it has been dubbed preheating. In preheating particles are produced very explosively (exponentially) but the momenta of these particles do not have a thermal distribution so you can't yet speak of the universe having a temperature.

To sum up, both preheating and reheating happen after inflation. In preheating particles are produced explosively by non-perturbative mechanisms (e.g. parametric resonance) but they aren't in thermal equilibrium (and in fact how they reach thermal equilibrium is a very non-trivial question). Reheating is a perturbaive process where a condensate of inflaton particles decays perturbatively and the decay products thermalize to give a hot soup of particles with a thermal distribution.

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