Compare · The Dark Universe

dRGT Massive Gravity vs Galileon Gravity

Large-Distance Modified Gravity · within family

	dRGT Massive Gravity Speculative	Galileon Gravity Rejected
Proposed	2011	2009
Key figures	Claudia de Rham, Gregory Gabadadze, Andrew Tolley	Alberto Nicolis, Riccardo Rattazzi, Enrico Trincherini
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.	Gravity gains an extra field, taken from the DGP braneworld, that can accelerate the expansion while switching itself off near stars and planets.
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	Late-time acceleration driven by the Galileon field, with no [[cosmological constant]] In the cubic version, gravitational potentials deepen at late times, which flips the sign of the correlation between [[cosmic microwave background]] temperature and nearby galaxies In the quartic and quintic versions, gravitational waves travel at a speed different from light at low redshift The extra force is screened inside the solar system and other gravitationally bound systems
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.	Once coupled to curved spacetime, the covariant Galileon keeps the Galileon interactions but breaks the exact galilean symmetry that defined the original model. Fits need a non-zero neutrino mass to match the data reasonably, around 0.5 eV in Renk and colleagues' analysis. Peirone and colleagues (2018) compared Bayesian evidence with ΛCDM and found covariant Galileon models strongly disfavoured by cosmological data.
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 speed-of-gravity problem: the quartic and quintic terms that let the Galileon fit cosmological data also change the speed of gravitational waves, and the cubic version alone fails the ISW test.
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dRGT Massive Gravity

2011 · Speculative

Galileon Gravity

2009 · Rejected

Proposed

2011

2009

Key figures

Claudia de Rham, Gregory Gabadadze, Andrew Tolley

Alberto Nicolis, Riccardo Rattazzi, Enrico Trincherini

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.

Gravity gains an extra field, taken from the DGP braneworld, that can accelerate the expansion while switching itself off near stars and planets.

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

Late-time acceleration driven by the Galileon field, with no [[cosmological constant]]
In the cubic version, gravitational potentials deepen at late times, which flips the sign of the correlation between [[cosmic microwave background]] temperature and nearby galaxies
In the quartic and quintic versions, gravitational waves travel at a speed different from light at low redshift
The extra force is screened inside the solar system and other gravitationally bound systems

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.

Once coupled to curved spacetime, the covariant Galileon keeps the Galileon interactions but breaks the exact galilean symmetry that defined the original model.
Fits need a non-zero neutrino mass to match the data reasonably, around 0.5 eV in Renk and colleagues' analysis.
Peirone and colleagues (2018) compared Bayesian evidence with ΛCDM and found covariant Galileon models strongly disfavoured by cosmological data.

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 speed-of-gravity problem: the quartic and quintic terms that let the Galileon fit cosmological data also change the speed of gravitational waves, and the cubic version alone fails the ISW test.

Reader vote

No votes yet