Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models

TL;DR

This paper derives stability conditions for the most general scalar-tensor theories, ensuring their cosmological viability, and applies these to extended Galileon dark energy models to identify stable, viable parameter spaces.

Contribution

It provides the first comprehensive stability criteria for Horndeski theories with two fluids and applies these to extended Galileon models, confirming their viability.

Findings

Stable parameter regions identified for extended Galileon models.

Models with tracker solutions can be free of ghosts and instabilities.

Numerical confirmation of the cosmological viability of these models.

Abstract

In the Horndeski's most general scalar-tensor theories with second-order field equations, we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar, tensor, and vector perturbations in the presence of two perfect fluids on the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Our general results are useful for the construction of theoretically consistent models of dark energy. We apply our formulas to extended Galileon models in which a tracker solution with an equation of state smaller than -1 is present. We clarify the allowed parameter space in which the ghosts and Laplacian instabilities are absent and we numerically confirm that such models are indeed cosmologically viable.