Stability Conditions for the Horndeski Scalar Field Gravity Model

TL;DR

This paper analyzes the stability of Horndeski scalar field gravity models, deriving constraints on the free functions in the Lagrangian using the positive energy theorem and other stability criteria, with implications for cosmology.

Contribution

It provides new stability conditions for Horndeski gravity models, especially constraining the form of the function G_3, and explores their cosmological applications.

Findings

G_3() is constrained to depend only on 

Relations among free functions are established

Stability criteria are applied to cosmological models

Abstract

We constrain the viable models of Horndeski gravity, written in its equivalent Generalised Galileon version, by resorting to the Witten positive energy theorem. We find that the free function $G_3(\phi, X)$ in the Lagrangian is constrained to be a function solely of the scalar field, $G_3(\phi)$, and relations among the free functions are found. Other criterion for stability are also analysed, such as the attractiveness of gravity, the Dolgov-Kawasacki instability and the energy conditions. Some applications for Cosmology are discussed