2015/06/30 by Cédric Deffayet, Cedric Deffayet, Gilles Esposito-Farèse +3 · 97 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Degrees of freedom (physics and chemistry) #Field (mathematics) #Geometry #Gravitation #Graviton #Hamiltonian (control theory) #Invariant (physics) #Mathematical physics #Mathematics #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Scalar field #Space time #Spacetime #Theoretical physics #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.92.084013
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 92(8) (American Physical Society) · 27 pages, no figure; v2: short explanation added below Eq. (42), improved Sec. II.B.2
arxiv created 2015/07/17 · openalex publication_date 2015/10/05 · arxiv updated 2015/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider Galileon models on curved spacetime, as well as the counterterms introduced to maintain the second-order nature of the field equations of these models when both the metric and the scalar are made dynamical. Working in a gauge-invariant framework, we first show how all the third-order time derivatives appearing in the field equations---both metric and scalar---of a Galileon model or one defined by a given counterterm can be eliminated to leave field equations which contain at most second-order time derivatives of the metric and of the scalar. The same is shown to hold for arbitrary linear combinations of such models, as well as their k-essence-like/Horndeski generalizations. This supports the claim that the number of degrees of freedom in these models is only 3, counting 2 for the graviton and 1 for the scalar. We comment on the arguments given previously in support of this claim. We then prove that this number of degrees of freedom is strictly lower than 4 in one particular such model by carrying out a full-fledged Hamiltonian analysis. In contrast to previous results, our analyses do not assume any particular gauge choice of restricted applicability.