Galileon Gravity

2009Alberto Nicolis, Riccardo Rattazzi, Enrico TrincheriniSpeculative11 primary sources, 11 established Reviewed October 17, 2026

Gravity gains a partner field with a special symmetry that can drive acceleration and hides itself near stars.

Rejected by observation

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general relativity: Einstein's theory of gravity, in which mass and energy curve spacetime, and we experience that curvature as gravitational pull.
scalar field: A field with one value at each point in space, like a temperature map. The inflaton is one example.
cosmological constant: A constant energy density of empty space. In general relativity, it drives the accelerated expansion of the universe. Often written as Lambda.
cosmic microwave background: The faint, uniform glow of light released about 380,000 years after the Big Bang, when the universe first became transparent.

§1 · The claim, in one sentence

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

Why this was rejected

▸Renk, Zumalacárregui, Montanari and Barreira (2017) found the cubic Galileon in 7.8 sigma tension with ISW data, which effectively rules it out.
▸GW170817 showed gravitational waves and light travel at the same speed to about one part in 10^15. Ezquiaga and Zumalacárregui (2017) found this rules out the quartic and quintic covariant Galileon as an explanation of late-time acceleration.
▸Baker and colleagues (2017) found the same measurement severely reduces the range of viable cosmological alternatives to general relativity.
▸Leloup and colleagues (2019) checked every cosmological fit of the full Galileon model against the GW170817 time delay and found all of them ruled out.

§2 · Why it might be true

Nicolis, Rattazzi and Trincherini started from the DGP model in a 2009 paper. Below the Hubble scale, every interesting departure DGP makes from general relativity is captured by one extra field. That field is a scalar field coupled equally to all matter, so it acts as part of gravity.

The authors kept the field and dropped the extra dimension. They required a 'galilean' symmetry, under which the field's gradient can shift by a constant. In four dimensions, only five interaction terms survive this symmetry without introducing ghosts.

Near stars and planets, the field's own interactions grow strong and it decouples from matter. This Vainshtein effect keeps solar-system tests in line with general relativity. On cosmic scales the theory has self-accelerating solutions, and unlike DGP's these are free of ghosts.

Deffayet, Esposito-Farèse and Vikman wrote the theory in curved spacetime, also in 2009. This covariant Galileon is the version cosmologists tested against data.

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 galilean symmetry limits the theory to five possible terms in four dimensions, which makes it tightly constrained.
It keeps DGP's self-accelerating solutions while removing the ghost instability that ruined them in DGP.
Chow and Khoury (2009) found its cosmology closely tracks the full five-dimensional DGP model, including a cosmological version of Vainshtein screening.
Renk and colleagues (2017), before GW170817, found quartic and quintic versions fitting CMB, BAO and ISW data about as well as ΛCDM.
De Rham and Gabadadze (2010) found the same cubic, quartic and quintic Galileon terms inside ghost-free massive gravity (sibling variant).

§3 · What you'd need to test it

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

§4 · Where it breaks

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.

Go deeper

The DGP decoupling limit reduces to a relativistic scalar π, universally coupled to matter, with derivative self-interactions. Nicolis, Rattazzi and Trincherini generalised it by demanding invariance under a shift of π's gradient by a constant vector. They argued this is the only generalisation of a universally coupled scalar that implements the Vainshtein effect robustly. In 4D the symmetry allows exactly five terms that give sizeable non-linearities without ghosts.

Minimally coupling the Galileon to a dynamical metric produces third-order derivatives in both the Galileon and metric equations. Deffayet, Esposito-Farèse and Vikman found a unique non-minimal coupling to curvature that restores second-order equations with no extra degree of freedom. Its generalisations are the Horndeski and beyond-Horndeski scalar-tensor theories that GW170817 later constrained.

Creminelli and Vernizzi required the gravitational-wave speed to stay equal to light for nearby cosmologies too, to avoid tuning. Of the three functions in quartic and quintic beyond-Horndeski theories, only one survives, a conformal coupling to the Ricci scalar in the Horndeski case. Sakstein and Jain combined GW170817 with the absence of strong equivalence-principle violation by the black hole in M87. Together these make the quartic Galileon cosmologically irrelevant.

▸§5 · Who built it, and when(11 sources, 11 established)

Alberto Nicolis

Theoretical physicist, Columbia University(birth year not published)

Nicolis analysed the DGP model with Rattazzi in 2004. In 2009, with Rattazzi and Trincherini, he turned its extra field into the Galileon, a four-dimensional modification of gravity.

“This symmetry constrains the structure of the π Lagrangian so much so that in 4D there exist only five terms that can yield sizable non-linearities without introducing ghosts.”

Nicolis, Rattazzi and Trincherini, 'The Galileon as a local modification of gravity' (2009), Phys. Rev. D 79, 064036, arXiv abstract

Riccardo Rattazzi(birth year not published)Co-author of the Galileon (2009) and of the 2003 and 2004 DGP consistency analyses, EPFL Lausanne
Enrico Trincherini(birth year not published)Co-author of the Galileon (2009), Scuola Normale Superiore, Pisa

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