p - adic Inflation

We construct approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory, a nonlocal theory with derivatives of all orders. Novel features include the existence of slow-roll solutions even when the slow-roll parameters, as usually defined, are much greater than unity, as well as the need for the Hubble parameter to exceed the string mass scale ms. We show that the theory can be compatible with CMB observations if g2 s/(ln p) ∼ 10−15, where gs is the string coupling, and if ms < 10Mp. A red-tilted spectrum is predicted, and an observably large tensor component is possible. The p-adic theory is shown to have identical inflationary predictions to a local theory with superPlanckian parameter values, but with the advantage that the p-adic theory is ultraviolet complete.