We study the cosmological meaning of duality symmetry by considering a
two dimensional model of string cosmology. We find that as seen by an
internal observer in this universe, the scale factor rebounds at the
self-dual length. This rebound is a consequence of the adiabatic expan
sion. Furthermore, in this situation there are four mathematically dif
ferent scenarios which describe physically equivalent universes which
are in fact undistinguishable. We also stress that R-duality suffices
to prove that all the possible evolutions present a maximun temperatur
e.