  In this paper, we study a big bounce universe typified by a non-singular big
bounce, as opposed to a singular big bang. This cosmological model can describe
radiation dominated early universe and matter dominated late universe in FRW
model. The connections between thermodynamics and gravity are observed here. In
the early stage of both cold and hot universes, we find there is only one
geometry containing a 4D de Sitter universe with a general state parameter. We
also find the form of the apparent horizon in the early universe strongly
depends on the extra dimension, which suggests that the influence of the extra
dimension could in principle be found in the early universe. Moreover, we show
that in the late stages of both cold and hot universes, the moment when the
apparent horizon begins to bounce keeps essentially in step with the behavior
of the cosmological scalar factor.
