  The scalar modes of the geometry induced by dimensional decoupling are
investigated. In the context of the low energy string effective action,
solutions can be found where the spatial part of the background geometry is the
direct product of two maximally symmetric Euclidean manifolds whose related
scale factors evolve at a dual rate so that the expanding dimensions first
accelerate and then decelerate while the internal dimensions always contract.
After introducing the perturbative treatment of the inhomogeneities, a class of
five-dimensional geometries is discussed in detail. Quasi-normal modes of the
system are derived and the numerical solution for the evolution of the metric
inhomogeneities shows that the fluctuations of the internal dimensions provide
a term that can be interpreted, in analogy with the well-known four-dimensional
situation, as a non-adiabatic pressure density variation. Implications of this
result are discussed with particular attention to string cosmological
scenarios.
