Horndeski extension of the minimal theory of quasidilaton massive gravity

TL;DR

This paper extends the minimal quasidilaton massive gravity theory by adding a Horndeski term, ensuring stability, the Vainshtein screening mechanism, and compatibility with local gravity tests, while maintaining a stable de Sitter solution.

Contribution

The paper introduces a Horndeski extension to the minimal quasidilaton theory that preserves degrees of freedom, stability, and screening, advancing the model's physical viability.

Findings

Stable self-accelerating de Sitter solutions across parameter ranges

Propagation speed of gravitational waves matches the speed of light

The extended theory maintains three physical degrees of freedom

Abstract

The minimal theory of quasidilaton massive gravity allows for a stable self-accelerating de Sitter solution in a wide range of parameters. On the other hand, in order for the theory to be compatible with local gravity tests, the fifth force due to the quasidilaton scalar needs to be screened at local scales. The present paper thus extends the theory by inclusion of a cubic Horndeski term in a way that (i) respects the quasidilaton global symmetry, that (ii) maintains the physical degrees of freedom in the theory being three, that (iii) can accommodate the Vainshtein screening mechanism and that still (iv) allows for a stable self-accelerating de Sitter solution. After adding the Horndeski term (and a k-essence type nonlinear kinetic term as well) to the precursor action, we switch to the Hamiltonian language and find a complete set of independent constraints. We then construct the minimal theory with three physical degrees of freedom by carefully adding a pair of constraints to the total Hamiltonian of the precursor theory. Switching back to the Lagrangian language, we study cosmological solutions and their stability in the minimal theory. In particular, we show that a self-accelerating de Sitter solution is stable for a wide range of parameters. Furthermore, as in the minimal theory of massive gravity, the propagation speed of the massive gravitational waves in the high momentum limit precisely agrees with the speed of light.