  In this paper we construct a discrete simulation of an expanding homogeneous
and isotropic space-time that expands via expansion of its basic elements to
figure out properties and characteristics of such a space-time and derive
conclusions. We prove that in such an expanding space-time, the geodesics are
curved and more precisely, they fluctuate on the boundaries of the expanding
basic elements. The non existence of privileged expansion direction leads to
the existence of an infinity of fluctuating geodesics between any two locations
in this space-time, that provides a prediction of polarization in geometric
optics, and a prediction of an earlier acceleration of the expansion as for the
cosmic inflation model. This simulation is a case study and an example of
space-time with variable topology using the principle of variation of topology
via a transformation that creates holes.
