The DBI Action, Higher-derivative Supergravity, and Flattening Inflaton Potentials

TL;DR

This paper investigates how higher-derivative operators in string theory effective actions modify scalar kinetic terms, leading to potential flattening that impacts inflationary predictions and CMB observables.

Contribution

It identifies supersymmetric dimension-eight operators affecting D-brane moduli and demonstrates their role in flattening inflaton potentials within supergravity.

Findings

Potential-dependent kinetic terms cause flattening of scalar potentials.

Flattening effects significantly alter inflationary CMB predictions.

Embedding of D-brane moduli into supergravity clarifies higher-derivative corrections.

Abstract

In string theory compactifications it is common to find an effective Lagrangian for the scalar fields with a non-canonical kinetic term. We study the effective action of the scalar position moduli of Type II D$p$-branes. In many instances the kinetic terms are in fact modified by a term proportional to the scalar potential itself. This can be linked to the appearance of higher-dimensional supersymmetric operators correcting the K\"ahler potential. We identify the supersymmetric dimension-eight operators describing the $\alpha'$ corrections captured by the D-brane Dirac-Born-Infeld action. Our analysis then allows an embedding of the D-brane moduli effective action into an $\mathcal N = 1$ supergravity formulation. The effects of the potential-dependent kinetic terms may be very important if one of the scalars is the inflaton, since they lead to a flattening of the scalar potential. We analyze this flattening effect in detail and compute its impact on the CMB observables for single-field inflation with monomial potentials.