Randall-Sundrum Model (1999): One Warped Extra Dimension

The Randall-Sundrum model, published in 1999 by Lisa Randall and Raman Sundrum, proposed that a single small extra dimension, strongly curved or “warped”, can explain why gravity is so much weaker than the other forces. Unlike earlier ideas, it needs neither many dimensions nor large ones: the warping does the work.

What the paper found

• One extra dimension, warped. Spacetime is five-dimensional, and the fifth dimension is a short interval bounded by two four-dimensional “branes”, like two parallel walls. Between them, spacetime is a slice of a curved geometry known as anti-de Sitter space.
• An exponential hierarchy. Because of the warping, any mass measured on one of the branes is reduced by an exponential factor that depends on the distance between the branes. A factor of about 10¹⁵ turns masses near the Planck scale, around 10¹⁹ GeV, into masses near a trillion electron volts (TeV), the scale of the weak force.
• No large numbers needed. The exponential means the underlying parameters only need to differ by a factor of about 50, not by the enormous ratios that other models require.
• Heavy gravitons at the TeV scale. The model predicts spin-2 particles, heavy copies of the graviton, with masses near a TeV that interact with ordinary particles with the strength of the weak force, not the feebleness of gravity. They would show up at a particle collider as distinctive resonances.

How they did it

The paper is theoretical. Randall and Sundrum found an exact solution of Einstein’s equations in five dimensions with two branes and appropriate vacuum energies, the “warped” metric, and showed how four-dimensional masses relate to the five-dimensional ones through the warp factor. The Standard Model particles live on one brane, where the warp factor makes everything light.

Why it mattered

The model offered a sharp alternative to the large extra dimensions of Arkani-Hamed, Dimopoulos and Dvali, published a year earlier. That proposal needs at least two extra dimensions, possibly as big as a millimeter. Randall and Sundrum needed one, and a small one. The two models predict different signals: ADD predicts a near-continuum of light graviton copies that carry energy away invisibly, while RS predicts a few heavy, separated resonances. The authors note that the constraints that apply to very large extra dimensions do not apply to their scenario.

Later in 1999 the same authors published a second paper, “An Alternative to Compactification” (Phys. Rev. Lett. 83, 4690), showing that a warped extra dimension could even be infinite in size and still reproduce ordinary four-dimensional gravity. Together, the two papers made warped geometry a standard tool of particle physics. They descend from Kaluza’s 1921 fifth dimension.

What we know now

As of October 2026, the Large Hadron Collider experiments have not reported a heavy graviton resonance of the kind the model predicts. The warped-dimension idea remains a hypothesis. Its four-dimensional backbone, the spacetime of Minkowski and Einstein’s general relativity, is established; the fifth dimension is not.

A different test probes extra dimensions that are not curled up: in 2018, GW170817 showed that gravitational waves crossing 40 megaparsecs did not lose strength to extra dimensions. Our explainer on the fourth dimension and extra dimensions collects the current limits.

Who wrote it

Lisa Randall was at Princeton University and MIT, and Raman Sundrum was at Boston University, when the paper was written. The model is widely called RS1, and the follow-up paper RS2.

Read the original

Randall, L., and Sundrum, R. (1999). “Large Mass Hierarchy from a Small Extra Dimension.” Physical Review Letters 83, 3370-3373. DOI: 10.1103/PhysRevLett.83.3370. Free to read on arXiv (hep-ph/9905221).