The fate of non-diagonalizable interactions in quasidilaton theory

TL;DR

This paper investigates the stability of solutions in quasidilaton theory when non-diagonalizable scalar-tensor interactions are included, revealing that such solutions are generally unstable or problematic within the Vainshtein radius.

Contribution

It extends previous stability analyses of quasidilaton theory to include non-diagonalizable interactions, identifying issues with solutions inside the Vainshtein radius.

Findings

Scalar modes exhibit gradient instabilities

Vector modes are infinitely strongly coupled

Vainshtein mechanism is absent in these solutions

Abstract

It has been shown that the spherically symmetric solutions in a subclass of quasidilaton theory are stable against all degrees of freedom and does not even exhibit superluminal propagation. These solutions can be found by switching off scalar-tensor interactions, which can not be removed by a local transformation. In this paper, we extend the analysis to quasidilaton theory, including non-diagonalizable scalar-tensor interactions. We show that all solutions inside the Vainshtein radius are problematic : the scalar mode in massive graviton suffers from gradient instabilities, the vector mode are infinitely strongly coupled vector perturbations, or the Vainshtein mechanism is absent.