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Cosmological Rescaling through Warped Space

Xingang Chen

TL;DR

The work proposes a cosmological mechanism where a moving anti-D3-brane in a warped extra dimension induces a non-comoving phase that exponentially rescales its world-volume, linking a geometric warp to the gravitational-electroweak hierarchy. It analyzes DBI dynamics in a warped AdS background, distinguishing comoving and non-comoving regimes and introducing a simple effective model with IR warp factors to quantify the rescaling. The main contribution is showing how brane self-gravity can alter embedding to convert local inhomogeneities into a hierarchy-compatible stretching, while addressing back-reaction, perturbations, and potential inflationary contexts. This approach bridges brane dynamics, warped geometry, and early-universe cosmology to offer a novel route to explain homogenization and scale separation.

Abstract

We discuss a scenario where at least part of the homogeneity on a brane world can be directly related to the hierarchy problem through warped space. We study the dynamics of an anti-D3-brane moving toward the infrared cut-off of a warped background. After a region described by the DBI action, the self-energy of the anti-D3-brane will dominate over the background. Then the world-volume scale of the anti-D3-brane is no longer comoving with the background geometry. After it settles down in the infrared end, the world-volume inhomogeneity will appear, to a Poincare observer, to be stretched by an exponentially large ratio. This ratio is close to that of the hierarchy problem between the gravitational and electroweak scales.

Cosmological Rescaling through Warped Space

TL;DR

The work proposes a cosmological mechanism where a moving anti-D3-brane in a warped extra dimension induces a non-comoving phase that exponentially rescales its world-volume, linking a geometric warp to the gravitational-electroweak hierarchy. It analyzes DBI dynamics in a warped AdS background, distinguishing comoving and non-comoving regimes and introducing a simple effective model with IR warp factors to quantify the rescaling. The main contribution is showing how brane self-gravity can alter embedding to convert local inhomogeneities into a hierarchy-compatible stretching, while addressing back-reaction, perturbations, and potential inflationary contexts. This approach bridges brane dynamics, warped geometry, and early-universe cosmology to offer a novel route to explain homogenization and scale separation.

Abstract

We discuss a scenario where at least part of the homogeneity on a brane world can be directly related to the hierarchy problem through warped space. We study the dynamics of an anti-D3-brane moving toward the infrared cut-off of a warped background. After a region described by the DBI action, the self-energy of the anti-D3-brane will dominate over the background. Then the world-volume scale of the anti-D3-brane is no longer comoving with the background geometry. After it settles down in the infrared end, the world-volume inhomogeneity will appear, to a Poincare observer, to be stretched by an exponentially large ratio. This ratio is close to that of the hierarchy problem between the gravitational and electroweak scales.

Paper Structure

This paper contains 6 sections, 9 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Comoving brane scale in the warped space
  3. Comoving region and back-reaction
  4. Non-comoving antibrane
  5. A simple model
  6. Discussion and open questions

Figures (2)

  • Figure 1: The dashed lines are the background geometry. For illustration, we compactify the three spatial dimensions of the antibrane and show only one of them on the graph. The wiggles indicate the inhomogeneities. In (A), the world-volume scale comoves with the background geometry, while in (B), the background geometry is negligible to the antibrane.
  • Figure 2: The solid lines are the effective geometry taking into account of the antibrane back-reaction. $r_{IR}$ is the IR cut-off, $r_0$ is the largest $r$-value the antibrane can go. $h_e$ and $h_0$ are the warp factors of this effective geometry at $r_{IR}$ and $r_0$, respectively. Both $h_e$ and $h_0$ are decreasing while the antibrane oscillates.