Gravitational backreaction of anti-D branes in the warped compactification

TL;DR

This paper develops a low-energy effective theory for gravity with anti-D branes in warped compactifications, highlighting the effects of their gravitational backreaction and the resulting potential energy behavior.

Contribution

It introduces a simplified 5D model capturing anti-D brane backreaction effects and analyzes the resulting gravitational potential and inflationary implications.

Findings

Anti-D brane tensions produce suppressed potentials.

The UV brane is dominated by dark radiation in the model.

Potential energy does not lead to inflation on the UV brane.

Abstract

We derive a low-energy effective theory for gravity with anti-D branes, which are essential to get de Sitter solutions in the type IIB string warped compactification, by taking account of gravitational backreactions of anti-D branes. In order to see the effects of the self-gravity of anti-D branes, a simplified model is studied where a 5-dimensional anti-de Sitter ({\it AdS}) spacetime is realized by the bulk cosmological constant and the 5-form flux, and anti-D branes are coupled to the 5-form field by Chern-Simon terms. The {\it AdS} spacetime is truncated by introducing UV and IR cut-off branes like the Randall-Sundrum model. We derive an effective theory for gravity on the UV brane and reproduce the familiar result that the tensions of the anti-D branes give potentials suppressed by the forth-power of the warp factor at the location of the anti-D branes. However, in this simplified model, the potential energy never inflates the UV brane, although the anti-D-branes are inflating. The UV brane is dominated by dark radiation coming from the projection of the 5-dimensional Weyl tensor, unless the moduli fields for the anti-D branes are stabilized. We comment on the possibility of avoiding this problem in a realistic string theory compactification.