Compare · The Dark Universe

dRGT Massive Gravity vs DGP Braneworld Gravity

Large-Distance Modified Gravity · within family

	dRGT Massive Gravity Speculative	DGP Braneworld Gravity Rejected
Proposed	2011	2000
Key figures	Claudia de Rham, Gregory Gabadadze, Andrew Tolley	Gia Dvali, Gregory Gabadadze, Massimo Porrati
In one sentence	De Rham, Gabadadze and Tolley gave the graviton a tiny mass without the Boulware-Deser ghost that sank earlier attempts, but the theory's simplest cosmological solutions are still unstable.	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.
Predictions	Gravity has a finite range set by the graviton mass, with a Yukawa-type fall-off at the largest distances Gravitational waves of different frequencies travel at slightly different speeds, because massive gravitons disperse On some self-accelerating branches, an effective cosmological constant proportional to the graviton mass squared drives late-time acceleration Near massive bodies, the Vainshtein mechanism hides the extra modes and recovers the predictions of general relativity	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]]
Where it breaks	D'Amico and colleagues (2011) showed that the constraint removing the ghost also forbids exactly homogeneous and isotropic universes. De Felice, Gumrukcuoglu and Mukohyama (2012) found every homogeneous and isotropic solution unstable, with at least one ghost. The self-accelerating open universes have no exactly flat limit, so the theory jumps discontinuously as spatial curvature goes to zero.	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.
Key unresolved problem	The missing-cosmology problem: the constraint that removes the ghost also forbids a flat expanding universe, and the curved ones that remain are unstable.	The ghost problem: the branch that accelerates without dark energy carries a negative-energy mode, and the ghost-free branch needs a cosmological constant to accelerate at all.
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dRGT Massive Gravity

2011 · Speculative

DGP Braneworld Gravity

2000 · Rejected

Proposed

2011

2000

Key figures

Claudia de Rham, Gregory Gabadadze, Andrew Tolley

Gia Dvali, Gregory Gabadadze, Massimo Porrati

In one sentence

De Rham, Gabadadze and Tolley gave the graviton a tiny mass without the Boulware-Deser ghost that sank earlier attempts, but the theory's simplest cosmological solutions are still unstable.

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.

Predictions

Gravity has a finite range set by the graviton mass, with a Yukawa-type fall-off at the largest distances
Gravitational waves of different frequencies travel at slightly different speeds, because massive gravitons disperse
On some self-accelerating branches, an effective cosmological constant proportional to the graviton mass squared drives late-time acceleration
Near massive bodies, the Vainshtein mechanism hides the extra modes and recovers the predictions of general relativity

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]]

Where it breaks

D'Amico and colleagues (2011) showed that the constraint removing the ghost also forbids exactly homogeneous and isotropic universes.
De Felice, Gumrukcuoglu and Mukohyama (2012) found every homogeneous and isotropic solution unstable, with at least one ghost.
The self-accelerating open universes have no exactly flat limit, so the theory jumps discontinuously as spatial curvature goes to zero.

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.

Key unresolved problem

The missing-cosmology problem: the constraint that removes the ghost also forbids a flat expanding universe, and the curved ones that remain are unstable.

The ghost problem: the branch that accelerates without dark energy carries a negative-energy mode, and the ghost-free branch needs a cosmological constant to accelerate at all.

Reader vote

No votes yet