Hagedorn inflation: open strings on branes can drive inflation

We demonstrate an inflationary solution to the cosmological horizon problem during the Hagedorn regime in the early universe. Here the observable universe is confined to three spatial dimensions (a three-brane) embedded in higher dimensions. The only ingredients required are open strings on D-branes at temperatures close to the string scale. No potential is required. Winding modes of the strings provide a negative pressure that can drive inflation of our observable universe. Hence the mere existence of open strings on branes in the early hot phase of the universe drives Hagedorn inflation, which can be either power law or exponential. We note the amusing fact that, in the case of stationary extra dimensions, inflationary expansion takes place only for branes of three or less dimensions.