The Dark Dimension (2023): A Micron-Sized Extra Dimension?

The dark dimension is a proposal by Miguel Montero, Cumrun Vafa and Irene Valenzuela, published in 2023, that the tiny observed value of dark energy implies a single extra dimension of space roughly a micrometer in size. It is a theoretical prediction built on conjectures about quantum gravity, and it has not been tested yet.

What the paper found

• One extra dimension, about a micrometer. Combining the measured strength of dark energy with conjectured rules for any consistent theory of quantum gravity, the authors predict exactly one extra “mesoscopic” dimension. Its size is of order 10^-6 meters, with an estimated range of about 0.1 to 10 micrometers.
• Why only one. Tabletop tests of gravity require any tower of new light states to be heavier than about 6.6 milli-electron volts. Separately, limits from the heating of old neutron stars allow a single extra dimension up to 44 micrometers but squeeze two extra dimensions below about 1.6 × 10^-4 micrometers. Only one extra dimension fits both constraints and the theory.
• A lower gravity scale. In the five-dimensional picture, the true strength of gravity becomes strong at about 10⁹ to 10¹⁰ GeV, far below the usual Planck scale.
• Neutrinos and more. The extra dimension naturally carries a tower of sterile neutrinos, and the authors connect it to the mass scale of ordinary neutrinos and to the scale of the Higgs field. They also speculate about links to the highest-energy cosmic rays.

How they did it

The paper belongs to the “Swampland” program, which tries to find rules that separate theories that can be completed into quantum gravity from those that cannot. One of those rules, the distance conjecture, says that when certain parameters become very small, an infinite tower of light particles must appear. The authors apply it to the cosmological constant, the simplest form of dark energy, which is famously tiny compared with natural expectations (the cosmological constant problem).

They then ask what kind of tower is allowed by experiments. The energy scale of dark energy, about 2.31 milli-electron volts, corresponds to a length of about 88 micrometers, uncomfortably close to the distances probed by the 2020 Eöt-Wash torsion-balance test, which the authors cite. Requiring consistency with that test and with astrophysical bounds singles out one extra dimension of micrometer size.

Why it mattered

The proposal ties together problems that are usually treated separately: the size of dark energy, the weakness of gravity, neutrino masses and the nature of dark matter. It also makes a concrete, testable claim. If the dark dimension exists, Newton’s law should fail at separations around a micrometer, a target for the next generation of short-range gravity experiments. It extends a line of thinking that runs from Kaluza’s fifth dimension through the large extra dimensions of 1998, which predicted at least two extra dimensions rather than one.

What we know now

As of October 2026, the dark dimension is an active research topic but has no experimental support. Its foundations are conjectures that are themselves debated, and its predictions sit just below the reach of current experiments: the best laboratory test reaches 52 micrometers, while the dark dimension is predicted at 0.1 to 10 micrometers. Theorists have since explored versions of the idea in which dark matter or a changing dark energy is linked to the extra dimension, which connects it to the DESI hints of evolving dark energy. Treat it as a well-motivated hypothesis, not a finding.

More context in our dark energy guide and our explainer on the fourth dimension and extra dimensions.

Who wrote it

Miguel Montero and Cumrun Vafa were at Harvard University’s Jefferson Physical Laboratory. Irene Valenzuela was at CERN’s Theoretical Physics Department and the Instituto de Física Teórica in Madrid.

Read the original

Montero, M., Vafa, C., and Valenzuela, I. (2023). “The dark dimension and the Swampland.” Journal of High Energy Physics 2023, article 22 (February 2023). DOI: 10.1007/JHEP02(2023)022. Open access, and free on arXiv (2205.12293), where it was first posted in May 2022.