  Our Universe is ruled by quantum mechanics and its extension Quantum Field
Theory (QFT). However, the explanations for a number of cosmological phenomena
such as inflation, dark energy, symmetry breakings, and phase transitions need
the presence of classical scalar fields. Although the process of condensation
of scalar fields in the lab is fairly well understood, the extension of results
to a cosmological context is not trivial. Here we investigate the formation of
a condensate - a classical scalar field - after reheating of the Universe. We
assume a light quantum scalar field produced by the decay of a heavy particle,
which for simplicity is assumed to be another scalar. We show that during
radiation domination epoch under certain conditions, the decay of the heavy
particle alone is sufficient for the production of a condensate. This process
is very similar to preheating - the exponential particle production at the end
of inflation. During matter domination epoch when the expansion of the Universe
is faster, the decay alone can not keep the growing trend of the field and the
amplitude of the condensate decreases rapidly, unless there is a self
interaction. This issue is particularly important for dark energy. We show that
quantum corrections of the self-interaction play a crucial role in this
process. Notably, they induce an effective action which includes inverse
power-law terms, and therefore can lead to a tracking behaviour even when the
classical self-interaction is a simple power-law of order 3 or 4. This removes
the necessity of having nonrenormalisable terms in the Lagrangian. If dark
energy is the condensate of a quantum scalar field, these results show that its
presence is deeply related to the action of quantum physics at largest
observable scales.
