Generalization of the Proca Action

By Lavinia Heisenberg. 2014

393 citations recorded by the source corpus.

We consider the Lagrangian of a vector field with derivative self-interactions with a priori arbitrary coefficients. Starting with a flat space-time we show that for a special choice of the coefficients of the self-interactions the ghost-like pathologies disappear. This constitutes the Galileon-type generalization of the Proca action with only three propagating physical degrees of freedom. The longitudinal mode of the vector field is associated to the usual Galileon interactions for a specific choice of the overall functions. In difference to a scalar Galileon theory, the generalized Proca field has more free parameters. We then extend this analysis to a curved background. The resulting theory is the Horndeski Proca action with second order equations of motion on curved space-times.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/9e8a3fe47a3478cccf165174baa49ae4bfd3450a

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In Astronomy and Astrophysics

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Citations in the corpus

Stellar structure models in modified theories of gravity: Lessons and challenges (2019, background): “The set of Lagrangians Li is characterized by several independent functions {G2,G3,G4,G5,G6,G7} which, in general, depend on both the vector potential and the field strength tensor (see [294, 295] for details).”
Cosmology in generalized Proca theories (2016, background): “Let us start with generalized Proca theories described by the four-dimensional action [70]”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, methodology): “Thus, the independent contractions will be in form of6 X = −AµAµ/2, F = −FµνFµν/4 and Y = AµAνFµαFνα [63, 169] and we can also rewrite the function in terms of these three scalar quantities (ignoring the partiy violating scalar quantity F̃ = Fµν F̃ µν ) L2 = f2(X,F, Y ) .”
Effective field theory of dark energy: A review (2019, methodology): “In parallel, the original EFT formalism has been also extended to include those theories with second-order derivative equations of motion with a vector or tensor additional field [51, 52], such as Generalised Proca [53], generalized Einstein-Aether [54] and massive bi-gravity [55].”
Generalized Proca action for an Abelian vector field (2015, methodology): “Previous works discussed parity conserving actions with N = 2 including up to 4 field derivatives ∂A, the so-called Ln, with n = 3, · · · , 5 [12], and n = 6 [36], n counting the number of field derivative plus two (this convention, bizarre in the vector case, is meaningful in the original galileon ”
Cosmological tests of modified gravity (2015, background): “ [73]. Also it is possible to construct galileon interactions for multiple scalar elds. See [75, 76, 77] for reviews and references therein. The galileon interactions can be also extended to vectors [78, 79, 80]. In curved space, if we covariantise the action naively by replacing the partial derivat”
Dark Energy in Light of Multi-Messenger Gravitational-Wave Astronomy (2018, background): “Proca theories have been generalized to include explicit gravitational interactions of a massive vector field (Heisenberg, 2014; Tasinato, 2014; Allys et al., 2016a; Beltran Jimenez and Heisenberg, 2016).”
Nonlocal gravity. Conceptual aspects and cosmological predictions (2017, background): “In contrast, modified gravity models that have been intensely studied in the literature in recent years involve either a free function ofR, as in f(R) theories [120], or a free function of −1R, as in the Deser-Woodard model [20], or even a set of arbitrary functions of a (hypothetical) scalar or mas”