  We show how a radiation dominated universe subject to space-time quantization
may give rise to inflation as the radiation temperature exceeds the Planck
temperature. We consider dispersion relations with a maximal momentum (i.e. a
mimimum Compton wavelength, or quantum of space), noting that some of these
lead to a trans-Planckian branch where energy increases with decreasing
momenta. This feature translates into negative radiation pressure and, in
well-defined circumstances, into an inflationary equation of state. We thus
realize the inflationary scenario without the aid of an inflaton field. As the
radiation cools down below the Planck temperature, inflation gracefully exits
into a standard Big Bang universe, dispensing with a period of reheating.
Thermal fluctuations in the radiation bath will in this case generate curvature
fluctuations on cosmological scales whose amplitude and spectrum can be tuned
to agree with observations.
