Inter-brane Interactions in Compact Spaces and Brane Inflation

TL;DR

This work analyzes inter-brane potentials in compact spaces by formulating and solving the Poisson equation with a jellium term, employing Green's functions and Ewald summation to capture compact-space effects on inflaton dynamics. It shows that the conventional D$\bar{D}$ inflation is not viable in the simplified moduli-stabilized setting, but branes-at-a-small-angle configurations evade the strong jellium contribution and can sustain slow-roll inflation after accounting harmonic corrections. The authors provide concrete estimates for various wrapping scenarios, showing viable slow-roll (and potentially rich phenomenology such as high-tension cosmic strings) and propose how moduli stabilization could alter these conclusions, highlighting the need for careful modeling of compactification dynamics. Overall, the paper offers a practical toolkit for evaluating brane-inflation potentials in compact spaces and demonstrates that small-angle brane configurations present a robust path to inflation within string-inspired setups.

Abstract

It was pointed out that brane-anti-brane inflation without warped geometry is not viable due to compactification effects (in the simplified scenario where the inflaton is decoupled from the compactification moduli). We show that the inflationary scenario with branes at a small angle in this simplified scenario remains viable. We also point out that brane-anti-brane inflation may still be viable under some special conditions. We also discuss a way to treat potentials in compact spaces that should be useful in the analysis of more realistic brane inflationary scenarios.

Figures (1)

• Figure 1: Two branes wrapping different cycles in a rectangular torus. The angle between the branes is $\tan\theta\simeq\theta=2u$.