Let $\overline{\rho}: G\longrightarrow \text{GL}_n(\mathbb{F}_p)$ be a residual representation of the Galois group of a number field. Let $R_{\overline{\rho}}^{\square,\text{univ}}$ be the universal framed deformation ring, which is a complete local noetherian $\mathbb{Z}_p$-algebra. $\text{Spf}(R_{\overline{\rho}}^{\square,\text{univ}})$ is the representing object of the quasifunctor $D_{\overline{\rho}}^{\square}$, which associates to an artinian local $\mathbb{Z}_p$-algebra, $A$, the groupoid which consists of representations $G\longrightarrow \text{GL}_n(A)$, whose reduction mod $p$ is $\rho$. The morphisms of this groupoid are parameterized by the group $\widehat{\text{PGL}}_n$, which is easier to describe as its functor of points: it is the kernel of $\text{GL}_n(A)\longrightarrow \text{GL}_n(\mathbb{F}_p)$. An element $p\in \widehat{\text{PGL}}_n(A)$ acts on a representation $\rho$ via $\rho\mapsto p\rho p^{-1}$.
I read in several places that if $\overline{\rho}$ is absolutely irreducible, then $\widehat{\text{PGL}}_n$ acts freely on $\text{Spf}(R_{\overline{\rho}}^{\square,\text{univ}})$. Why is this the case?
