Healthy degenerate theories with higher derivatives

By H. Motohashi, K. Noui, T. Suyama, Masahide Yamaguchi, D. Langlois. 2016

180 citations recorded by the source corpus.

In the context of classical mechanics, we study the conditions under which higher-order derivative theories can evade the so-called Ostrogradsky instability. More precisely, we consider general Lagrangians with second order time derivatives, of the form L(̈ϕa, ϕ̇a, ϕa; qi, qi) with a = 1,⋯,n and i = 1,⋯,m. For n = 1, assuming that the qi's form a nondegenerate subsystem, we confirm that the degeneracy of the kinetic matrix eliminates the Ostrogradsky instability. The degeneracy implies, in the Hamiltonian formulation of the theory, the existence of a primary constraint, which generates a secondary constraint, thus eliminating the Ostrogradsky ghost. For n > 1, we show that, in addition to the degeneracy of the kinetic matrix, one needs to impose extra conditions to ensure the presence of a sufficient number of secondary constraints that can eliminate all the Ostrogradsky ghosts. When these conditions that ensure the disappearance of the Ostrogradsky instability are satisfied, we show that the Euler-Lagrange equations, which involve a priori higher order derivatives, can be reduced to a second order system.

View Paper: https://www.semanticscholar.org/paper/ef251ba583fd96a3d5f7efcca0a3ab92ae2cfa00

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Citations in the corpus

Horndeski theory and beyond: a review (2019, background): “ties of tensor or scalar modes [176, 177] (see also [181, 182] for more about this instability issue). The idea of degenerate theories can be extended to include more than one higher derivative ﬁelds [183, 184], though it seems challenging to construct concrete nontrivial examples of a multi-scalar ”
Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order (2016, background): “For Lagrangians depending on the accelerations of several variables, the degeneracy of the Lagrangian is not sufficient to eliminate the multiple Ostrogradsky ghosts and extra conditions must be imposed, as shown in [21] for classical mechanics systems (see also [22] for a slightly different approac”
Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review (2018, background): “In [19] and [20], the previous analysis was extended to more general Lagrangians containing several variables with accelerations, namely of the form L(φ̈, φ̇, φ; q̇, q) (α = 1, · · · , n; i = 1, · · · ,m) , (3.”