Cosmological evolution in DHOST theories

TL;DR

This paper investigates the stability and cosmological solutions of DHOST theories, emphasizing the importance of degeneracy to avoid higher order derivatives, and identifies conditions for stable de Sitter attractors compatible with matter coupling.

Contribution

It explicitly demonstrates how degeneracy in DHOST theories prevents higher order derivatives in equations and analyzes stability conditions for cosmological solutions with matter coupling.

Findings

De Sitter attractors can be achieved without instabilities in certain DHOST models.

Degeneracy ensures equations remain second order despite higher derivatives.

Conditions for stability are compatible with self-acceleration and matter dominance eras.

Abstract

In the context of Degenerate Higher-Order Scalar-Tensor (DHOST) theories, we study cosmological solutions and their stability properties. In particular, we explicitly illustrate the crucial role of degeneracy by showing how the higher order homogeneous equations in the physical frame (where matter is minimally coupled) can be recast in a system of equations that do not involve higher order derivatives. We study the fixed points of the dynamics, finding the conditions for having a de Sitter attractor at late times. Then we consider the coupling to matter field (described for convenience by a k-essence Lagrangian) and find the conditions to avoid gradient and ghost instabilities at linear order in cosmological perturbations, extending previous work. Finally, we apply these results to a simple subclass of DHOST theories, showing that de Sitter attractor conditions, no ghost and no gradient instabilities conditions (both in the self-accelerating era and in the matter dominated era) can be compatible.