# Failures of homogeneous and isotropic cosmologies in Extended Quasi-Dilaton Massive Gravity

## TL;DR

This paper investigates the stability and physical consistency of extended quasi-dilaton massive gravity models in cosmological settings, revealing challenges in approaching fixed points and conditions for avoiding ghost modes.

## Contribution

It provides a detailed stability analysis of fixed points in extended quasi-dilaton massive gravity and examines conditions for ghost-free solutions.

## Key findings

- Traditional fixed point is only approached with fine-tuned initial conditions.
- A second fixed point with $\dot^0=0$ can be an attractor under certain conditions.
- The Boulware-Deser ghost is only eliminated under special initial conditions.

## Abstract

We analyze the Extended Quasi-Dilaton Massive Gravity model around a Friedmann-Lema\^itre-Robertson-Walker cosmological background. We present a careful stability analysis of asymptotic fixed points. We find that the traditional fixed point cannot be approached dynamically, except from a perfectly fine-tuned initial condition involving both the quasi-dilaton and the Hubble parameter. A less-well examined fixed-point solution, where the time derivative of the 0-th St\"uckelberg field vanishes $\dot\phi^0=0$, encounters no such difficulty, and the fixed point is an attractor in some finite region of initial conditions. We examine the question of the presence of a Boulware-Deser ghost in the theory. We show that the additional constraint which generically allows for the elimination of the Boulware-Deser mode is only present under special initial conditions. We find that the only possibility corresponds to the traditional fixed point and the initial conditions are the same fine-tuned conditions that allow the fixed point to be approached dynamically.