de Sitter Versus Anti-de Sitter in Horndeski-Like Gravity

Abstract

The general solutions of Horndeski-like gravity that can interpolate between the de Sitter and anti-de Sitter regimes are presented. In particular, the first-order formalism with two scalar fields is developed, and considering a black hole ansatz with flat slicing, three different cases, namely exponential, vacuum, and smooth superpotential solutions, with no Minkowski extrema are investigated. Furthermore, these solutions show that a Renormalization Group flow is established, and a turnaround in the warp factor is obtained, where the transition is bounded by the area low. The ideal regimes to trap gravity, which are constructed using the holographic function, which provides stable and unstable regimes to localize gravity are discussed. Finally, it is shown that no ghost appear and that the matter sector that violates the $c$-theorem is physical.