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Classical Stability of the Galileon
High Energy Physics - Theory · Submitted 8 Jun 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In fact, when considering generic solutions there are no choices of free parameters in the Galileon theory that will lead to absolute stability except the DGP choice.
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The abstract, sentence by sentence
We consider the classical equations of motion for a single Galileon field with generic parameters in the presence of non-relativistic sources. We introduce the concept of absolute stability of a theory: if one can show that a field at a single point---like infinity for instance---in spacetime is stable, then stability of the field over the rest of spacetime is guaranteed for any positive energy source configuration. The Dvali-Gabadadze-Porrati (DGP) model is stable in this manner, and previous studies of spherically symmetric solutions suggest that certain classes of the single field Galileon (of which the DGP model is a subclass) may have this property as well. We find, however, that when general solutions are considered this is not the case. In fact, when considering generic solutions there are no choices of free parameters in the Galileon theory that will lead to absolute stability except the DGP choice. Our analysis indicates that the DGP model is an exceptional choice among the large class of possible single field Galileon theories. This implies that if general solutions (non-spherically symmetric) exist they may be unstable. Given astrophysical motivation for the Galileon, further investigation into these unstable solutions may prove fruitful.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the classical equations of motion for a single Galileon field with generic parameters in the presence of non-relativistic sources. | contribution 0.55 | 0.81 | 0.02 | asserted 0.64 |
| s1 | We introduce the concept of absolute stability of a theory: if one can show that a field at a single point---like infinity for instance---in spacetime is stable, then stability of the field over the rest of spacetime is guaranteed for any positive energy source configuration. | contribution 0.79 | 0.75 | 0.07 | asserted 0.96 |
| s2 | The Dvali-Gabadadze-Porrati (DGP) model is stable in this manner, and previous studies of spherically symmetric solutions suggest that certain classes of the single field Galileon (of which the DGP model is a subclass) may have this property as well. | background 0.98 | 0.08 | 0.04 | hedged possibility 0.72 |
| s3 | We find, however, that when general solutions are considered this is not the case. | result 1.00 | 0.91 | 0.28 | asserted 1.00 |
| s4 | In fact, when considering generic solutions there are no choices of free parameters in the Galileon theory that will lead to absolute stability except the DGP choice. | result 1.00 | 0.94 | 0.82 | asserted 1.00 |
| s5 | Our analysis indicates that the DGP model is an exceptional choice among the large class of possible single field Galileon theories. | interpretation 0.88 | 0.86 | 0.32 | asserted 0.84 |
| s6 | This implies that if general solutions (non-spherically symmetric) exist they may be unstable. | interpretation 1.00 | 0.70 | 0.18 | hedged possibility 1.00 |
| s7 | Given astrophysical motivation for the Galileon, further investigation into these unstable solutions may prove fruitful. | future work 1.00 | 0.11 | 0.04 | hedged possibility 0.98 |
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The paper
Original abstract
We consider the classical equations of motion for a single Galileon field with generic parameters in the presence of non-relativistic sources. We introduce the concept of absolute stability of a theory: if one can show that a field at a single point---like infinity for instance---in spacetime is stable, then stability of the field over the rest of spacetime is guaranteed for any positive energy source configuration. The Dvali-Gabadadze-Porrati (DGP) model is stable in this manner, and previous studies of spherically symmetric solutions suggest that certain classes of the single field Galileon (of which the DGP model is a subclass) may have this property as well. We find, however, that when general solutions are considered this is not the case. In fact, when considering generic solutions there are no choices of free parameters in the Galileon theory that will lead to absolute stability except the DGP choice. Our analysis indicates that the DGP model is an exceptional choice among the large class of possible single field Galileon theories. This implies that if general solutions (non-spherically symmetric) exist they may be unstable. Given astrophysical motivation for the Galileon, further investigation into these unstable solutions may prove fruitful.
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References
How the literature uses it
7 arXiv papers cite this in 10 sentences
Papers citing it · 5 sentences without a confident label
Uses its method or tool 1 paper
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This is the approach adopted by Nicolis et al. [ref] [ref] in studying the stability of the DGP model.
Moving Stable Solitons in Galileon Theory · The Solutions and Their Stability · 0.94
Cites it as background 4 papers
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In particular, one can investigate the universe evolution and late-time acceleration [ref] , inflation [ref] and non-Gaussianities [ref] , the reheating of the post-inflationary universe [ref] , the growth history [ref] , the cosmological bounce [ref] , the cosmological perturbations [ref] , the spherical solutions [ref] , the stability issues [ref] , and also he can use observational data in order to constrain the parameters of the theory [ref] .
Dynamical analysis of generalized Galileon cosmology · Introduction · 0.95
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[ref] for more details in this direction.
Primordial non-Gaussianity from ultra slow-roll Galileon inflation · Introduction · 0.96
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This work led to the proliferation of phenomenological applications of Galileon fields to gravity, quantum field theory and cosmology [ref] .
Galileon inflation evades the no-go for PBH formation in the single-field framework · Introduction · 0.88
What it cites · 4 sentences without a confident label
Cites as support 2 papers
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Thanks to the Galileon invariance, the $ℒ_n$'s above are not renormalized under loop corrections, and terms with fewer derivatives acting on the $π$ field are not generated quantum mechanically [ref] (a similar proof holds for the multi-field Galileons [ref] ).
Strong Interactions and Stability in the DGP Model · The Galileon · 0.97
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In particular, upon estimating the one loop effective action one can see that for classical solutions with large non-linearities quantum effects are small provided gradients are mild $≪Λ$ [ref] .
Classical and Quantum Consistency of the DGP Model · The Galileon · 0.97
Cites as background 2 papers
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This is the DGP-like case and has been thoroughly discussed in [ref] .
Classical and Quantum Consistency of the DGP Model · $c_5=0$, $c_30$ · 0.87
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A quick word of clarification: when we make reference to the DGP model, we mean not strictly the coefficients that come from the 4-d effective field theory associated with the extra-dimensional model put forth by [ref] , but rather the class of theories where $c̃_1=0$, $c̃_2>0$, $c̃_4=0$, and $c̃_5=0$.
4D Gravity on a Brane in 5D Minkowski Space · The Galileon · 0.81
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