  It is known that four-dimensional cosmologies exhibiting transient phases of
acceleration can be obtained by compactifications of low-energy effective
string or M-theory on time-varying manifolds. In the four-dimensional theory,
the acceleration can be attributed to a quintessential scalar field with a
positive effective potential. Recently, Townsend has conjectured that the
potentials obtained by such compactifications cannot give rise to late-time
accelerating universes which possess future event horizons. Such a `no-go'
result would be desirable, since current string or M-theory seems unable to
provide an adequate description of space-times with future event horizons. In
this letter, we provide a proof of this conjecture for a class of warped
compactifications with a single scalar modulus parametrising the volume of the
compactification manifold.
