Irreducibility conjecture for Misiurewicz polynomials

Fix an integer $d\geq 2$, let $m\geq 2$ and $n\geq 1$, and let $\zeta\neq 1$ be a $d$-th root of unity. For the Misiurewicz polynomial $G_{d,m,n}^{\zeta}(c)$ defined by the parameter iterates of $f(z)=z^d+c$, the irreducibility conjecture. $G_{d,m,n}^{\zeta}$ is irreducible over $\mathbb{Q}(\zeta)$. This is presented as the analogue over $\mathbb{Q}(\zeta)$ of a conjecture attributed to Milnor concerning related polynomials over $\mathbb{Q}$; no resolution is supplied here.