Induced gravity on intersecting brane-worlds Part I: Maximally symmetric solutions

TL;DR

The paper investigates six-dimensional intersecting brane-worlds with induced gravity on codimension-one branes and their intersection, seeking four-dimensional gravity without compactification and possible self-accelerating expansion. By analyzing maximally symmetric configurations and applying Israel junction conditions, the authors derive relations among bulk and brane parameters and identify self-accelerating branches that exhibit a see-saw gravity pattern, where the UV and IR modification scales are set by $M_6$ and $M_6^2/M_4$, respectively. They find new self-accelerating solutions in 6D and extend the analysis to higher codimensions, showing that viability worsens as the number of extra dimensions grows due to increasingly small fundamental scales and persistent ghost issues. They also present self-tuning configurations where the vacuum energy at the intersection does not curve 4D spacetime, suggesting a way to address the cosmological constant problem without compactifying extra dimensions. The work provides a framework for obtaining 4D gravity from infinite-volume extra dimensions while highlighting challenges such as ghosts and experimental bounds on higher-dimensional Planck scales, motivating further study of FRW cosmology on the branes and at their intersection.

Abstract

We explore models of intersecting brane-worlds with induced gravity terms on codimension one branes and on their intersection. Maximally symmetric solutions for the branes and the intersection are found. We find new self-accelerating solutions. In a 6d spacetime, the solutions realize the see-saw modification of gravity where the UV scale of the modification to 4d gravity is determined by 6d Planck scale given by $M_6 \sim 10^{-3}$eV and the IR scale of the modification is determined by $M_6^2/M_4 \sim H_0 \sim 10^{-42}$ GeV where $H_0$ is present-day Hubble scale. We find that it is increasingly difficult to construct phenomenologically viable models in higher-dimensional spacetime due to the necessity to have the lower value for the fundamental Planck scale to realize the late time acceleration. It is found that the system also admits self-tuning solutions where the tension at the intersection does not change the geometry of the intersection. The induced gravity terms can avoid the necessity to compactify the extra dimensions. Finally, we discuss the possibility to have ordinary matter at the intersection, without introducing any regularisation, using the induced gravity terms.