Exploring gravitational theories beyond Horndeski

By J. Gleyzes, D. Langlois, F. Piazza, F. Vernizzi. 2014

424 citations recorded by the source corpus.

We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in ref. [1]. As they generalize Horndeski theories, or “generalized” galileons, we call them G3. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under a disformal redefinition of the metric. Remarkably, these theories are preserved by disformal transformations that depend on the scalar field gradient, which also allow to map subfamilies of G3 into Horndeski theories.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ea8f12fcb6e4326e8666beba949b2ac63d2f6be9

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Citations in the corpus

Gravitational wave decay into dark energy (2018, methodology): “n holds if ~m 4 is large enough to play any role in modifying gravity and potentially aecting large-scale structure measurements. In the framework of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories [24,25], setting ~m 4 = 0 (or equivalently H = 0, where H is dened in eq. (47)) and requiring GWs to ”
Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review (2018, methodology): “• The family of Beyond Horndeski theories is stable under disformal transformations with C = C(φ) and D = D(φ,X), as demonstrated in [12].”
Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability (2015, methodology): “Note that these findings are consistent with the results of [15] showing the correspondence between theories beyond Horndeski and Horndeski theories via disformal transformations for restricted subclasses of Lagrangians.”
Healthy degenerate theories with higher derivatives (2016, background): “Recently it has been pointed out that one can find healthy extensions of Horndeski theories [7, 8], whose Euler-Lagrange equations involve higher order derivatives (see also [9] for an earlier example of theory “beyond Horndeski”).”
Cosmological tests of modified gravity (2015, methodology): “lar quantities: KK ; SK K ; RR ; R ; UR K : (55) The Lagrangian that leads to second order equations of motion can be expressed in terms of the geometric scalars introduced above as [82, 92] L= A 2(N;t) + A 3(N;t)K+ A 4(N;t)(K2 S ) + B 4(N;t)R +A 5(N;t)K 3 + B 5(N;t)(U KR=2) ; (56) where K 3 K3 3KK ”
Stellar structure models in modified theories of gravity: Lessons and challenges (2019, background): “For the subset of beyond Horndeski theories corresponding to the so-called G3 galileons [137] (a generalization of the covariant quartic galileon G2 [140]), it has been shown by Koyama and Sakstein [141] that the generalized Lane-Emden equation in this case takes the form 1 ξ2 d dξ [”
Extended scalar-tensor theories of gravity (2016, background): “In the literature, the unitary gauge is frequently used to study extended theories of Horndeski [4, 5, 21].”
Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations (2016, background): “In [6], it was shown that disformal transformations of Horndeski theories with A = 1 lead to the extensions beyond Horndeski proposed in [5].”
Horndeski theory and beyond: a review (2019, background): “ reduced to a second-order system for the scale factor and the scalar ﬁeld. Clearly, the Horndeski theory is included in class Ia. Another important particular case is (a subclass of) the GLPV theory [47, 48] satisfying A2 = −A1 = fX +XA3 ⇒ A4 = −A3, A5 = 0. (115) In this case one has two arbitrary ”
A unifying description of dark energy (2014, methodology): “Our ADM approach is also at the core of several recent works [17, 18] and is very useful for the theories beyond Horndeski that we proposed in [19, 20] (see also [21, 22, 23, 24, 25]).”
Effective field theory of dark energy: A review (2019, methodology): “This assumption can be relaxed considering a frame where the gravitational interaction between the additional scalar DoF and the matter fields is explicit [74, 75, 76, 77].”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “The construction of this type of beyond Horndeski interactions has created a lot of activities in the literature (see for instance [159, 160, 161, 162]).”
Asymptotically flat black holes in Horndeski theory and beyond (2017, background): “realized that Horndeski theory was not the only physically relevant alternative [9, 10] for scalartensor theories.”
Effective description of higher-order scalar-tensor theories (2017, methodology): “The above quadratic action extends the one derived in [4] and written in terms of the dimensionless time-dependent functions αA (introduced in [16] and [17]) in [7], with the addition of four new functions of time: the parameter αL, and the three parameters βA that characterize the terms containing ”