Extended vector-tensor theories

Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke

doi:10.1088/1475-7516/2017/01/002

Cited by 120 publications

(132 citation statements)

References 55 publications

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“…Field redefinitions of this kind have been studied in tensorial notation in [49]. They have also been used to screen the cosmological vector field [50] and to study Weyl geometry as a vector-tensor theory [51,52].…”

Section: B Mixing With Spin-1 Fieldsmentioning

confidence: 99%

Field redefinitions in theories beyond Einstein gravity using the language of differential forms

2017

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We study the role of field redefinitions in general scalar-tensor theories. In particular, we first focus on the class of field redefinitions linear in the spin-2 field and involving derivatives of the spin-0 mode, generically known as disformal transformations. We start by defining the action of a disformal transformation in the tangent space. Then, we take advantage of the great economy of means of the language of differential forms to compute the full transformation of Horndeski's theory under general disformal transformations. We obtain that Horndeski's action maps onto itself modulo a reduced set of non-Horndeski Lagrangians. These new Lagrangians are found to be invariant under disformal transformation that depend only in the first derivatives of the scalar. Moreover, these combinations of Lagrangians precisely appear when expressing in our basis the constraints of the recently proposed Extended Scalar-Tensor (EST) theories. These results allow us to classify the different orbits of scalar-tensor theories invariant under particular disformal transformations, namely the special disformal, kinetic disformal and disformal Horndeski orbits. In addition, we consider generalizations of this framework. We find that there are possible well-defined extended disformal transformations that have not been considered in the literature. However, they generically cannot link Horndeski theory with EST theories. Finally, we study further generalizations in which extra fields with different spin are included. These field redefinitions can be used to connect different gravity theories such as multi-scalar-tensor theories, generalized Proca theories and bi-gravity. We discuss how the formalism of differential forms could be useful for future developments in these lines.PACS numbers: 04.50. Kd, 98.80.Cq, 95.36.+x,

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Section: B Mixing With Spin-1 Fieldsmentioning

confidence: 99%

Field redefinitions in theories beyond Einstein gravity using the language of differential forms

2017

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“…Their cosmological perturbations, in the framework of the effective theory of dark energy (see e.g., [18]), are studied in [19]. Analogously, similar constructions for vector interactions were introduced in [20] and a classification for degenerate vector-tensor theories up to quadratic order was given in [21].…”

Section: Introductionmentioning

confidence: 99%

Beyond Lovelock gravity: Higher derivative metric theories

et al. 2018

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We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than 2 degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories." Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector.

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“…In a recent work, [6], the authors have shown that the galileon-like terms cannot be introduced in a flat spacetime under the assumption of U (1) invariance, although in a curved space-time the vector Horndeski term can be allowed [7]. Once we abandon the U (1) gauge invariance, one can investigate a broad class of theories of massive vector field [8][9][10][11][12][13]. Theoretical developments in the theories of massless/massive vector fields may have interesting impacts for cosmology, such as cosmic inflation [14], the generation of primordial magnetic fields on large scales (see [15] for a review), or dark energy (see also e.g.…”

Section: Introductionmentioning

confidence: 99%

On metric transformations with a U(1) gauge field

Felice

Naruko

2020

Phys. Rev. D

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We study metric transformations including not just the field strength tensor of a U (1) gauge field, but also its dual tensor. We first consider an arbitrary symmetric matrix built up with these two tensors in the metric transformation. It turns out the form of transformation reduces to a quite simple form on imposing the parity evenness of the transformed metric and by utilising the Cayley-Hamilton theorem as well as other useful identities. Interestingly, the same form for the transformation was recently argued in the process of seeking for a generic metric transformation but without the inclusion of the dual tensor.

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Extended vector-tensor theories

Cited by 120 publications

References 55 publications

Field redefinitions in theories beyond Einstein gravity using the language of differential forms

Field redefinitions in theories beyond Einstein gravity using the language of differential forms

Beyond Lovelock gravity: Higher derivative metric theories

On metric transformations with a U(1) gauge field

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