REVIEW
Galileons in the Sky
Cosmology and Nongalactic Astrophysics · Submitted 24 Apr 2012 · 74 references
Pith's verdict: A competent, well-organized review that maps DGP, New Massive Gravity, ghost-free massive gravity, and the Lovelock-braneworld construction onto the Galileon; the only real blemish is an inverted scaling in Eqs. (64)-(65).
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Referee report
The paper
The paper claims
The review argues that Galileon scalar fields unify the extra scalar mode of DGP, New Massive Gravity, and ghost-free massive gravity, and that a non-renormalization theorem makes them viable for inflation and cosmic acceleration.
The reading
What carries the argument
The load-bearing object is the Galileon Lagrangian, built from four interactions $L_2$ through $L_5$ in four dimensions, whose equations of motion stay second order and which are invariant under $varphitovarphi+c+v_mu x^mu$. The Vainshtein mechanism is the physical payoff: inside a dense source the kinetic term is dominated by higher derivatives, the canonically normalized fluctuation couples weakly to matter, and the fifth force is screened. The non-renormalization theorem is the quantum payoff: loop corrections depend on $partial Z/Z$ and come with extra derivatives, so they do not regenerate the Galileon operators and the strong-coupling scale $Lambda$ is not radiatively driven up to the cutoff. In massive gravity the same structure is encoded in the tensor $K_{munu}=delta_{munu}-sqrt{delta_{munu}-g_{mualpha}H^{alphanu}}$, whose tuned potential removes the Boulware-Deser ghost and reduces to Galileon interactions in the decoupling limit.
Extended reading notes
Core claim
The central claim is that Galileon fields supply a unified description of the helicity-0 mode in DGP, New Massive Gravity, and ghost-free massive gravity, and that their shift and Galilean symmetries, together with second-order equations of motion, make them radiatively stable even when their interactions are strong. From that claim the review derives two cosmological possibilities. In massive gravity, the scalar can source acceleration with a Hubble rate set by the graviton mass, or it can cancel a large vacuum energy and leave a flat geometry. In the early universe, the same non-renormalized interactions can drive inflation and generate non-Gaussianities whose shapes differ from standard slow roll or DBI. The review presents these as motivations and branch structures, not as a completed fit to data.
Load-bearing premise
The central cosmological conclusions rely on treating the decoupling limit, and a flat-space non-renormalization theorem, as a reliable guide to the full theory, where the helicity-0 and helicity-2 modes couple again and curved-space corrections enter.
Editorial extensions
If this is right
- If the non-renormalization theorem holds, the Galileon interactions can be large at $\Lambda \ll M_{\rm Pl}$ without quantum corrections destroying the Vainshtein mechanism.
- In ghost-free massive gravity, the self-accelerating branch can give $H^2\sim m^2$ with stable scalar fluctuations for a range of parameters, so cosmic acceleration need not come from a cosmological constant.
- The degravitating branch can keep geometry flat in the presence of an arbitrarily large vacuum energy by having the scalar absorb it, although the screening scale then tracks the size of that energy.
- Galileon inflation can produce non-Gaussianities from dimension-7 and higher operators, with shapes that differ from standard slow-roll and DBI inflation.
Reading between the lines
- If the degravitating branch's strong-coupling scale is tied to the cosmological constant it absorbs, then screening a vacuum energy much above $10^{-3}\,{\rm eV}$ would conflict with fifth-force bounds unless the dimensionless coefficients are tuned; that suggests the branch is a proof of principle rather than a ready solution to the cosmological constant problem.
- The review's own caveat that superluminal propagation can arise wherever the Vainshtein mechanism operates suggests a generic test: map the parameter region where the scalar sound speed exceeds unity and check whether it overlaps the region needed for acceleration or inflation.
- The coupling $\partial_\mu\varphi\,\partial_\nu\varphi\,T^{\mu\nu}$ vanishes for static spherical sources but not for relativistic ones, so weak lensing and structure-growth observables are the natural place to look for a signature that distinguishes these models from a cosmological constant.
- Because the non-renormalization argument is established in flat space, a curved-space calculation that changes the scaling of the one-loop effective action would also change which inflationary and late-time parameter ranges remain under control.
Original abstract
We review the different frameworks in which Galileon scalar fields have been seen to emerge such an in DGP, New Massive Gravity and Ghost-free massive Gravity and emphasize their relation with the Lovelock invariant in braneworld models. The existence of a non-renormalization theorem for Galileon scalar fields makes them especially attractive candidates for inflation as well as for late-time acceleration. In particular we review the self-accelerating and degravitating branches of solutions present in Galileon models when arising from Massive Gravity and discuss their phenomenology.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We review the different frameworks in which Galileon scalar fields have been seen to emerge such an in DGP, New Massive Gravity and Ghost-free massive Gravity and emphasize their relation with the Lovelock invariant in braneworld models. The existence of a non-renormalization theorem for Galileon scalar fields makes them especially attractive candidates for inflation as well as for late-time acceleration. In particular we review the self-accelerating and degravitating branches of solutions present in Galileon models when arising from Massive Gravity and discuss their phenomenology.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We review the different frameworks in which Galileon scalar fields have been seen to emerge such an in DGP, New Massive Gravity and Ghost-free massive Gravity and emphasize their relation with the Lovelock invariant in braneworld models. | contribution 0.57 | 0.17 | 0.10 | asserted 0.95 |
| s1 | The existence of a non-renormalization theorem for Galileon scalar fields makes them especially attractive candidates for inflation as well as for late-time acceleration. | background 0.78 | 0.08 | 0.20 | asserted 0.94 |
| s2 | In particular we review the self-accelerating and degravitating branches of solutions present in Galileon models when arising from Massive Gravity and discuss their phenomenology. | contribution 0.97 | 0.28 | 0.14 | asserted 0.91 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
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- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
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- R cross-paper relations
References
How the literature uses it
65 arXiv papers cite this in 73 sentences
Papers citing it · 17 sentences without a confident label
Cites it as support 1 paper
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However, if we ignore power-law divergences this tuning is technically natural, as loops involving galileon operators only generate terms with 3 or more derivatives per field (see e.g., [ref] ).
Beyond the Cosmological Standard Model · Simplest example: the cubic galileon · 0.98
Cites it as background 52 papers
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The Galileon system has been studied both analytically and numerically (see e.g. [ref] ).
Scalar Radiation with a Quartic Galileon · Numerical Implementation · 1.00
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In the so-called decoupling limit [ref] , the structure of self-accelerating configurations is relatively easy to study, and the theory exhibits the explicit Galileon symmetry in the scalar sector, resulting in an attractive model from the point of view of stability under classical and quantum corrections (see [ref] for reviews).
Vector instabilities and self-acceleration in the decoupling limit of massive gravity · Introduction · 0.98
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The action of the Galileon model was first derived in [ref] , by generalizing the four-dimensional effective action of the Dvali-Gabadadze-Porrati (DGP) model [ref] .
Nonlinear structure formation in the Cubic Galileon gravity model · Introduction · 0.93
What it cites · 48 sentences without a confident label
Builds on 1 paper
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This possibility was then further investigated by [ref] if the leading interactions from operators of the form $(ϕ)^2 (^2 ϕ)^n$ vanish, the next to leading order operators of the form $(^2 ϕ)^n$ become the dominant ones.
Galilean symmetry in the effective theory of inflation: new shapes of non-Gaussianity · Galileon Inflation · 0.84
Uses the method or tool of 1 paper
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It will be useful to construct the following quantity, [ref] =(g,H)=δ-√(δ- g^μαH_αν) .
Resummation of Massive Gravity · Decoupling limit · 0.84
Cites as support 3 papers
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Indeed, one can show explicitly that unitarity is still preserved, [ref] .
Ghost free Massive Gravity in the St\"uckelberg language · Beyond the decoupling limit · 0.99
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Indeed, one can show explicitly that unitarity is still preserved, [ref] .
Helicity Decomposition of Ghost-free Massive Gravity · Beyond the decoupling limit · 0.99
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Indeed, one can show explicitly that unitarity is still preserved, [ref] .
Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation · Beyond the decoupling limit · 0.99
Cites as background 21 papers
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One of the breakthrough of the DGP model, [ref] , was the realization that the Universe could be accelerating without the presence of any cosmological constant or other source of “dark-energy" but sourced by the graviton very own dofs and in particular by its helicity-0 mode, [ref] .
4D Gravity on a Brane in 5D Minkowski Space · Self-acceleration in DGP and Galileons · 0.85
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One of the breakthrough of the DGP model, [ref] , was the realization that the Universe could be accelerating without the presence of any cosmological constant or other source of “dark-energy" but sourced by the graviton very own dofs and in particular by its helicity-0 mode, [ref] .
Cosmology on a Brane in Minkowski Bulk · Self-acceleration in DGP and Galileons · 0.85
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We therefore only focus on the model of Galileon Inflation presented in [ref] , and refer to [ref] for further work on Galileon Inflation, G-Inflation and the generation of non-gaussianities in these classes of models and to Refs. [ref] for work on Galilean Genesis.
G-inflation: inflation driven by the Galileon field · Galileon Inflation · 0.90
Discussion
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