Right or left, back or forth, up or down, earlier or later: the everyday world our senses experience is, at least apparently, 3+1-dimensional. One would then think that extra dimensions beyond the usual 3+1 spacetime ones, an exciting and common ingredient in many science fiction stories, should be indeed left to science fiction novelists. It turns out, however, that extra dimensions are not at all uncommon in actual physics theories. For several decades, scientists have toyed with the idea of introducing extra dimensions to solve some of the long-standing problems of physics. One such puzzle, known as the “hierarchy problem”, is why gravity is so much weaker than the other three fundamental forces of nature (the strong, weak, and electromagnetic forces).

In some of these extra dimensional theories all particles and forces, except gravity, are confined to the usual 3+1-dimensional spacetime. Gravity, on the other hand, would feel these extra dimensions and travel through them. The “leaking” of gravity into extra dimensions might even help explain why it is so much weaker than all the other known forces. Our senses would not be aware of the fifth dimension, much as the two-dimensional inhabitants of Flatland were not aware of the existence of the third dimension. This is the idea behind “brane cosmology” or “brane-world models”, where our four-dimensional spacetime is restricted to a “brane” which lives in a higher-dimensional space known as the “bulk”. Among the most popular brane-worlds we find the Randall-Sundrum models (named after Lisa Randall and Raman Sundrum, see this paper and this other paper for their original work) where our 3+1-dimensional spacetime is surrounded by an infinite 5-dimensional anti-de Sitter spacetime (or AdS_{5 }for short). This AdS_{5 }spacetime is characterized by its curvature radius: the larger the curvature radius, the more AdS_{5 }looks flat (think of the Earth: the larger the Earth radius, the more it appears flat).

This all sounds exciting and – perhaps – looks like it belongs more to the science fiction realm than to reality. However, physicists have good reasons to take these types of conjectures seriously. The question is then: can we ever hope to observationally probe these extra dimensions? A lot of smart people have thought about ways of testing the existence of extra dimensions, for example by looking at particular signatures at colliders such as the LHC or searching for modifications to Newton’s law at short distances (if you are curious, have a look at this review for more information). It turns out there is another way to hunt for extra dimensions, based on an idea by Robert Caldwell and David Langlois, that makes use of a source of gravitational waves. You need to be able to detect both the gravitational waves and the light released from the event. This is the basis of what is known as multi-messenger astronomy. Since (in Einstein’s theory of General Relativity) gravitational waves and light both travel at the same speed — you guessed it, the speed of light! — one would expect the two signals to reach us at the same time. However, if brane-world extra dimensions exist, gravitational waves can take a shortcut in the fifth dimension and actually reach us before the photons do.

Sounds crazy? On August 17, 2017 LIGO and Virgo detected the gravitational waves released during the last minutes of a binary neutron star merger (GW170817) . Within two seconds, Fermi and INTEGRAL also detected a short gamma-ray burst released by the same neutron star merger event. The near-simultaneous arrival of the two signals was used to set very stringent constraints on deviations from Einstein’s general relativity (see for instance this review if you are interested).

Thanks to these two amazing detections, it has also been possible to hunt for extra dimensions using gravitational waves for the first time. OKC researchers, **Katie Freese**, **Luca Visinelli**, and **Sunny Vagnozzi**, in collaboration with **Nadia Bolis** who was visiting OKC from CEICO in Prague, used the measurements of the time-delay between the gravitational and the electromagnetic signal to put constraints on the curvature radius of the fifth dimension, assuming that gravitational waves travelled along a shortcut in the fifth dimension. They did a careful statistical analysis of the time-delay, taking into account uncertainties in the emission of the gamma-ray burst from the neutron star and the impact of large-scale structure between us and the neutron star on the propagation of the gravitational waves. They concluded that no evidence for non-zero curvature radius could be found and set a 95% confidence level upper limit of 1.997 Megaparsecs on the curvature radius of the fifth dimension. In other words, we can be 95% sure that the curvature radius of the fifth dimension is less than about 6.5 million light-years large.

The results, which appeared in November in the arXiv preprint repository were then published in March in the journal Physical Review D. The tools to reproduce the analysis are publicly available on Github.

This is the first time that researchers have been able to hunt for extra dimensions using gravitational waves. We like to think it’s no accident that this work was done at the OKC, an institute named after the late Oskar Klein who is considered by many to be the father of extra dimensional theories.

Text by OKC graduate student researcher Sunny Vagnozzi.