Monodromy in the CMB: Gravity waves and string inflation

Abstract

We present a simple mechanism for obtaining large-field inflation, and hence a gravitational wave signature, from string theory compactified on twisted tori. For nil manifolds, we obtain a leading inflationary potential proportional to ${\ensuremath{\phi}}^{2/3}$ in terms of the canonically normalized field $\ensuremath{\phi}$, yielding predictions for the tilt of the power spectrum and the tensor-to-scalar ratio, ${n}_{s}\ensuremath{\approx}0.98$ and $r\ensuremath{\approx}0.04$ with 60 e-foldings of inflation; we note also the possibility of a variant with a candidate inflaton potential proportional to ${\ensuremath{\phi}}^{2/5}$. The basic mechanism involved in extending the field range---monodromy in $D$-branes as they move in circles on the manifold---arises in a more general class of compactifications, though our methods for controlling the corrections to the slow-roll parameters require additional symmetries.