In this paper, we study the possibility of building a model of the
oscillating universe with quintom matter in the framework of 4-dimensional
Friedmann-Robertson-Walker background. Taking the two-scalar-field quintom
model as an example, we find in the model parameter space there are five
different types of solutions which correspond to: (I) a cyclic universe with
the minimal and maximal values of the scale factor remaining the same in every
cycle, (II) an oscillating universe with its minimal and maximal values of the
scale factor increasing cycle by cycle, (III) an oscillating universe with its
minimal and maximal values of the scale factor decreasing cycle by cycle, (IV)
an oscillating universe with its scale factor always increasing, and (V) an
oscillating universe with its scale factor always decreasing.Comment: 14 pages, 6 figures, accepted by PL