  We investigate a cosmological model, based on the Salam-Sezgin
six-dimensional supergravity theory and on previous work by Anchordoqui,
Goldberg, Nawata, and Nu\~nez. Assuming a period of warm inflation, we show
that it is possible to extend the evolution of the model back in time, to
include the inflationary period, thus unifying inflation, dark matter, and dark
energy within a single framework. Like the previous authors, we were not able
to obtain the full dark matter content of the Universe from the Salam-Sezgin
scalar fields. However, even if only partially successful, this work shows that
present-day theories, based on superstrings and supergravity, may eventually
lead to a comprehensive modelling of the evolution of the Universe. We find
that the gravitational-wave spectrum of the model has a non-constant negative
slope in the frequency range 10^(-15)-10^6 rad/s, and that, unlike standard
(cold) inflation models, it shows no structure in the MHz/GHz range of
frequencies.
