Well-posedness of Cubic Horndeski Theories

We study the local well-posedness of the initial value problem for cubic Homdeski theories. Three different strongly hyperbolic modifications of the Arnowitt-Deser-Misncr formulation of the Einstein equations are extended to cubic Horndeski theories in the "weak field" regime. In the first one, the equations of motion are rewritten as a coupled elliptic-hyperbolic system of partial differential equations. The second one is based on the Baumgarte-Shapiro-Shibata-Nakamura formulation with a generalized Bona-Mass6 slicing (covering the 1 + log slicing) and nondynamical shift vector. The third one is an extension of the CCZ4 formulation with a generalized Bona-Mass6 slicing (also covering the 1 + log slicing) and a gamma driver shift condition. This final formulation may be particularly suitable for applications in nonlinear numerical simulations.