Can codimension-two branes solve the cosmological constant problem?

TL;DR

This paper investigates whether codimension-two braneworlds can dynamically solve the cosmological constant problem, finding that in Einstein gravity they do not self-tune to zero but can reproduce standard cosmology.

Contribution

It provides explicit solutions with thick branes in a 6D model and analyzes the relation between brane tension and deficit angle, showing the lack of self-tuning in Einstein gravity.

Findings

Standard FRW cosmology is recovered with thick branes.

The deficit angle relates to brane matter as $ riangle=2\pi G_6( ho-3 p)$.

No evidence of dynamical relaxation of the cosmological constant in Einstein gravity.

Abstract

It has been suggested that codimension-two braneworlds might naturally explain the vanishing of the 4D effective cosmological constant, due to the automatic relation between the deficit angle and the brane tension. To investigate whether this cancellation happens dynamically, and within the context of a realistic cosmology, we study a codimension-two braneworld with spherical extra dimensions compactified by magnetic flux. Assuming Einstein gravity, we show that when the brane contains matter with an arbitrary equation of state, the 4D metric components are not regular at the brane, unless the brane has nonzero thickness. We construct explicit 6D solutions with thick branes, treating the brane matter as a perturbation, and find that the universe expands consistently with standard Friedmann-Robertson-Walker (FRW) cosmology. The relation between the brane tension and the bulk deficit angle becomes $\Delta=2\pi G_6(\rho-3 p)$ for a general equation of state. However, this relation does not imply a self-tuning of the effective 4D cosmological constant to zero; perturbations of the brane tension in a static solution lead to deSitter or anti-deSitter braneworlds. Our results thus confirm other recent work showing that codimension-two braneworlds in nonsupersymmetric Einstein gravity do not lead to a dynamical relaxation of the cosmological constant, but they leave open the possibility that supersymmetric versions can be compatible with self-tuning.