Slow Roll in Brane Inflation

TL;DR

This work investigates slow-roll in string-theory inflation by exploiting a Kahler-invariant formulation of the scalar potential, arguing that flat directions for brane-position moduli are generic in brane inflation scenarios. It analyzes two concrete compactifications, $K3\times T^2/Z_2$ and $T^6/Z_2$, showing how shift symmetry can protect the inflaton direction at leading order and how T-duality constrains the Kahler potential. The paper surveys the full inflationary potential as a sum $V=V^F+V^D+V_{SB}$ and discusses the impact of $\alpha′$ corrections, D-terms, and inter-brane interactions on slow-roll, highlighting that higher-order corrections and moduli stabilization crucially influence $\eta$. It also connects these theoretical insights to complete models (e.g., KKLT) and potential observational implications, such as cosmic strings and CMB features, while proposing that shift symmetry renders slow-roll a generic possibility in this framework. The analysis provides a practical methodology to assess slow-roll viability in complex string compactifications and suggests directions for testing through dual descriptions and warped-throat constructions.

Abstract

We address the issue of slow-roll in string theory models of inflation. Using a Kähler transformation and results from the D3-D7 model, we show why we expect flat directions to be present and slow-roll to be possible in general. We connect with earlier discussions of shift symmetry for $T^6/Z_2$ and $K3\times T^2/Z_2$ compactifications. We also collect various contributions to the inflationary potential and discuss their importance for slow-roll. We include a few simple checks of the form of the Kahler potential on $T^6/Z_2$ using T-duality.

Figures (1)

• Figure 1: Simple possibilities for inflation. (a) The D3 moves along a flat direction, parallel to a D7 brane. (b) Whether $D \bar{D}$ or D3-D7 inflation occurs depends on the arrangement of branes.