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For a fixed mod $p$ automorphic Galois representation, $p$-adic automorphicGalois representations lifting it determine points in universal deformationspace. In the case of modular forms and under some technical conditions,B\"{o}ckle showed that every component of deformation space contains a smoothmodular point, which then implies their Zariski density when coupled with theinfinite fern of Gouv\^{e}a-Mazur. We generalize B\"{o}ckle's result to thecontext of polarized Galois representations for CM fields, and to twodimensional Galois representations for totally real fields. More specifically,under assumptions necessary to apply a small $R = \mathbb{T}$ theorem and anassumption on the local mod $p$ representation, we prove that every irreduciblecomponent of the universal polarized deformation space contains an automorphicpoint. When combined with work of Chenevier, this implies new results on theZariski density of automorphic points in polarized deformation space indimension three.

On automorphic points in polarized deformation rings