We compute the spectrum of cosmological perturbations in a scenario in which
inflation is driven by radiation in a non-commutative space-time. In this
scenario, the non-commutativity of space and time leads to a modified
dispersion relation for radiation with two branches, which allows for
inflation. The initial conditions for the cosmological fluctuations are
thermal. This is to be contrasted with the situation in models of inflation in
which the accelerated expansion of space is driven by the potential energy of a
scalar field, and in which the fluctuations are of quantum vacuum type. We find
that, in the limit that the expansion of space is almost exponential, the
spectrum of fluctuations is scale-invariant with a slight red tilt. The
magnitude of the tilt is different from what is obtained in a usual
inflationary model with the same expansion rate during the period of inflation.
The amplitude also differs, and can easily be adjusted to agree with
observations.Comment: 7 pages, 1 figur