Limiting the Number of Extra Dimensions with Shortcuts

TL;DR

This paper proposes a braneworld model allowing shortcuts for gravitons in higher dimensions and uses gravitational wave observations to set upper limits on the number of extra dimensions, refining previous constraints.

Contribution

It analytically derives horizon radii in a braneworld model and establishes observational bounds on the number of extra dimensions using gravitational wave data.

Findings

Upper limit of d ≤ 9 dimensions from GW170817/GRB 170817A

Adjusted upper limits to d ≤ 4 and d ≤ 12 considering observational errors

Large extra dimensions are not yet ruled out by current torsion balance measurements

Abstract

In higher-dimensional theories, a graviton propagating in the bulk can follow a shorter path, known as a shortcut, compared to a photon propagating in a four-dimensional spacetime. Thus by combining the observations of gravitational waves and their electromagnetic counterparts, one can gain insights into the structure and number of extra dimensions. In this paper, we construct a braneworld model that allows the existence of shortcuts in a $D(=4+d)$-dimensional spacetime. It has been proven that the equations for modeling brane cosmology recover the standard Friedmann equations for the late universe. We derive analytically the graviton and photon horizon radii on the brane under the low-energy limit. With the event GW170817/GRB 170817A, we find that the number of extra dimensions has an upper limit of $d\leq9$. Because of the errors in the source redshift and time delay, this upper limit can be shifted to $d\leq4$ and $d\leq12$. Although with the joint constraint on the $\text{AdS}_{D}^{~}$ radius from torsion balance measurements, theories with large $d$ are not yet ruled out, our work provides a new way to limit the number of extra dimensions.