DGP Braneworld Gravity

2000Gia Dvali, Gregory Gabadadze, Massimo PorratiSpeculativeAlso answers, Ch.01 Before the Universe8 primary sources, 8 established Reviewed October 17, 2026

Our universe is a brane in an infinite fifth dimension, and gravity leaks into it at cosmic distances.

Rejected by observation

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brane: A higher-dimensional surface on which strings can end. Our universe may be a 3-brane embedded in a larger space.
dark energy: The unknown component driving the accelerating expansion of the universe, making up about 68 percent of its energy.
cosmological constant: A constant energy density of empty space. In general relativity, it drives the accelerated expansion of the universe. Often written as Lambda.
bulk: The higher-dimensional space in which lower-dimensional branes are embedded.
cosmic microwave background: The faint, uniform glow of light released about 380,000 years after the Big Bang, when the universe first became transparent.
general relativity: Einstein's theory of gravity, in which mass and energy curve spacetime, and we experience that curvature as gravitational pull.

§1 · The claim, in one sentence

Our universe is a brane in a five-dimensional space, and at distances near the size of the observable universe gravity behaves five-dimensionally; one solution accelerates the expansion but is unstable.

Why this was rejected

▸Charmousis, Gregory, Kaloper and Padilla (2006) found a ghost on the self-accelerating branch for any value of the brane tension. They concluded these solutions are not a reliable benchmark for cosmic acceleration.
▸Fang and colleagues (2008) found that flat self-accelerating DGP fits CMB, supernova and Hubble-constant data 5.3 sigma worse than ΛCDM. Adding spatial curvature still leaves it 4.8 sigma worse.
▸Lombriser, Hu, Fang and Seljak (2009) found that data require brane tension or a cosmological constant on both branches, with no evidence for DGP's own modifications.

§2 · Why it might be true

Dvali, Gabadadze and Porrati proposed in 2000 that our universe is a brane in five-dimensional space. The extra dimension is flat and infinitely large. At short distances, gravity on the brane follows the familiar four-dimensional law. At very large distances, it behaves like gravity in five dimensions.

Deffayet showed in 2001 that this setup allows two kinds of expanding universe. On one branch the expansion speeds up at late times with no dark energy at all. This self-accelerating branch made DGP an explicit example of gravity doing the work of dark energy.

DGP borrows its picture from the braneworld models of Chapter 1. Dvali also co-authored the 1998 ADD proposal of large extra dimensions. ADD and Randall-Sundrum use extra dimensions to explain why gravity is so weak. DGP uses one infinite extra dimension to change gravity at cosmic distances instead.

The family stance

These theories try to explain cosmic acceleration by changing gravity at distances comparable to the observable universe, instead of adding dark energy. There gravity either spreads into an extra dimension or behaves as if its carrier particle, the graviton, has a tiny mass. Near stars and planets the extra effects switch off, so solar-system tests still agree with general relativity. The best-known self-accelerating versions face serious stability and observational problems.

§2.5 · Evidence

The model gives a simple geometric setup where four-dimensional gravity emerges on a brane inside an infinite fifth dimension.
Nicolis and Rattazzi (2004) showed that the Vainshtein effect restores agreement with precise tests of general relativity near massive bodies.
Charmousis, Gregory, Kaloper and Padilla (2006) found the normal branch of solutions free of ghosts in their perturbative analysis, so those solutions are safe at large distances.
Its four-dimensional limit, a single field with unusual self-interactions, became the starting point for the Galileon (sibling variant).

§3 · What you'd need to test it

Below a crossover distance, gravity on the brane follows the ordinary four-dimensional inverse-square law
On the self-accelerating branch, the expansion accelerates at late times without a cosmological constant
Perturbations that leak into the bulk change how structure grows, adding extra cosmic microwave background anisotropy on the largest angular scales
Near massive bodies, an extra mode that bends the brane is screened by the Vainshtein effect, restoring the predictions of general relativity

§4 · Where it breaks

Luty, Porrati and Rattazzi (2003) found that with the crossover near the Hubble length, the theory becomes strongly coupled below about 1000 km.
The self-accelerating branch contains a ghost, a mode with negative energy that makes spacetime unstable.
The ghost-free normal branch only accelerates with brane tension or a cosmological constant, which brings dark energy back.

Go deeper

DGP includes an intrinsic curvature term, a four-dimensional Ricci scalar, in the action of a brane sitting in a Minkowski bulk. Deffayet derived the resulting brane-Friedmann equations for a Z_2-symmetric metric. For small Hubble radii both classes of solution track ordinary Friedmann-Lemaître-Robertson-Walker cosmology. As the Hubble radius grows, one class goes fully five-dimensional and the other becomes a self-inflationary solution with late acceleration.

Luty, Porrati and Rattazzi traced the strong coupling to a longitudinal 'eaten Goldstone' mode, as in massive gravity. The mode gets a small kinetic term only by mixing with transverse graviton polarizations. Its strong-coupling length scales as (λ_DGP^2 / M_P)^(1/3), about 1000 km when λ_DGP is near the Hubble length. Nicolis and Rattazzi then rewrote the model as a boundary effective action for the brane bending mode π, the field the Galileon later generalised.

Charmousis and colleagues pinned down the ghost. For positive brane tension it is the helicity-0 part of the lightest massive graviton, of mass 0 < m^2 < 2H^2. For negative tension it is the radion, and at zero tension a mixture of both. Lombriser and colleagues bound the crossover scale at H_0 r_c > 3 at 95% confidence, including spatial-curvature uncertainty.

Compared with the Chapter 1 braneworlds: ADD uses compact extra dimensions and Randall-Sundrum a warped slice of anti-de Sitter space, both aimed at the hierarchy problem. DGP keeps the bulk flat and infinite, and the brane's own curvature term is what keeps gravity four-dimensional at short range.

▸§5 · Who built it, and when(8 sources, 8 established)

Gia Dvali

Theoretical physicist, Ludwig Maximilian University and Max Planck Institute, Munich1964-

Dvali co-authored the 1998 ADD proposal of large extra dimensions. In 2000, with Gabadadze and Porrati, he proposed a braneworld where gravity leaks into an infinite fifth dimension.

“We suggest a mechanism by which four-dimensional Newtonian gravity emerges on a 3-brane in 5D Minkowski space with an infinite size extra dimension.”

Dvali, Gabadadze and Porrati, '4-D gravity on a brane in 5-D Minkowski space' (2000), Phys. Lett. B 485, 208, abstract

Gregory Gabadadze(birth year not published)Co-author of the DGP model (2000) and of dRGT massive gravity (2011), New York University
Massimo Porrati(birth year not published)Co-author of the DGP model (2000) and of the 2003 analysis showing it becomes strongly coupled near 1000 km, New York University

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