Stable solutions in Horndeski theory

The construction of completely stable solutions within the framework of Horndeski theory is significantly limited by the "no-go" theorem. However, in this article, we reveal a novel approach to constructing stable solutions within the general Horndeski framework. Our research focuses on scenarios in which the previously studied unitary gauge has a singularity. We construct a spatially flat, stable solution described by general relativity in combination with non-canonical scalar fields. Following this, we analyze the effect of perturbations from an anisotropic background on these solutions' stability. This investigation provides valuable information about the dynamics of cosmological models using non-canonical scalar fields.