Shortcut in codimension-2 brane cosmology in light of GW170817

TL;DR

This paper investigates how extra dimensions in a six-dimensional Anti-de Sitter spacetime affect gravitational wave propagation and time delays, providing constraints on the AdS radius based on GW170817 observations.

Contribution

It derives the gravitational horizon radius in codimension-2 brane cosmology and constrains the AdS radius using gravitational wave and electromagnetic observations.

Findings

Upper limit on AdS6 radius from GW170817 data.

Stronger constraints on AdS radius for high-redshift GW events.

Predicted bounds for future GW detectors like DECIGO and BBO.

Abstract

In this paper, our universe is regarded as a codimension-2 brane embedded in a noncompact six-dimensional Anti-de Sitter (AdS) spacetime. We derive the gravitational horizon radius on the brane under the low-energy approximation, which reflects how the extra dimensions cause the shortcut effect of gravitational waves (GWs). We also study the time delay between a GW signal and an electromagnetic (EM) wave signal in the low-redshift limit by combining with the joint observations of GW170817/GRB 170817A, which gives an upper limit to the $\text{AdS}_{6}^{~}$ radius as $\ell^{2}_{~} \lesssim 3.84\,\text{Mpc}^{2}_{~}$. For a high-redshift source, the time delay is converted into the discrepancy between the source redshift derived from the GW signal and the one derived from the EM counterpart. It is found that if one expects to detect the EM counterpart of a high-redshift GW event within a reasonable observation time, it requires a stronger constraint on the $\text{AdS}_{6}^{~}$ radius. Our research shows that the $\text{AdS}_{6}^{~}$ radius should satisfy $\ell^{2}_{~}\lesssim0.02\,\text{Mpc}^{2}_{~}$ for the DECIGO and BBO.