  In string models with "brane supersymmetry breaking" exponential potentials
emerge at (closed-string) tree level but are not accompanied by tachyons.
Potentials of this type have long been a source of embarrassment in flat space,
but can have interesting implications for Cosmology. For instance, in ten
dimensions the logarithmic slope |V'/V| lies precisely at a "critical" value
where the Lucchin--Matarrese attractor disappears while the scalar field is
\emph{forced} to climb up the potential when it emerges from the Big Bang. This
type of behavior is in principle perturbative in the string coupling, persists
after compactification, could have trapped scalar fields inside potential wells
as a result of the cosmological evolution and could have also injected the
inflationary phase of our Universe.
