  In order not to be in conflict with observations it is crucial that extra
dimensions, if they exist, are stable. It is shown that in the context of
homogeneous extra dimensions, this can easily be achieved during both (4D)
radiation and vacuum energy dominated eras of the cosmological evolution.
During matter domination, however, there is no such possibility even for a very
general class of stabilization mechanisms. Even if extra dimensions could be
stabilized during matter domination, it is argued that they are generically
time-varying during any transition period, such as the one from radiation to
matter domination.
