Codimension-two branes in six-dimensional supergravity and the cosmological constant problem

TL;DR

This paper examines six-dimensional supergravity models with codimension-two branes to assess their potential in solving the cosmological constant problem, finding that they do not self-tune as hoped.

Contribution

It provides a detailed perturbative analysis showing that these models do not achieve self-tuning of the cosmological constant.

Findings

Geometry remains time-dependent under perturbations.

No static or self-tuning solutions are found.

Time evolution prevents relaxation to a static state.

Abstract

We investigate in detail recent suggestions that codimension-two braneworlds in six dimensional supergravity might circumvent Weinberg's no-go theorem for self-tuning of the cosmological constant. The branes are given finite thickness in order to regularize mild singularities in their vicinity, and we allow them to have an arbitrary equation of state. We study perturbatively the time evolution of the solutions by solving the equations of motion linearized around a static background. Even allowing for the most general possibility of warping and nonconical singularities, the geometry does not relax to a static solution when the brane stress-energies are perturbed. Rather, both the internal and external geometries become time-dependent, and the system does not exhibit any self-tuning behavior.