Stability of Homogeneous Extra Dimensions

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.