  In the present paper we study the evolution of the modes of a scalar field in
a cyclic cosmology. In order to keep the discussion clear, we study the
features of a scalar field in a toy model, a Friedman-Robertson-Walker universe
with a periodic scale factor, in which the universe expands, contracts and
bounces infinite times, in the approximation in which the dynamic features of
this universe are driven by some external factor, without the backreaction of
the scalar field under study. In particular, we show that particle production
exhibits features of the cyclic cosmology. Also, by studying the Berry phase of
the scalar field, we show that contrarily to what is commonly believed, the
scalar field carries information from one bounce to another in the form of a
global phase which occurs to be generically non-zero. {The Berry phase is then
evaluated numerically in the case of the effective Loop Quantum Cosmology
closed Universe. We observe that Berry's phase is nonzero, but that in the
quantum regime the particle content is non-negligible.
