Smoothness conjecture for the ordinary deformation ring

Let $R_\rho^{\mathrm{ord}}$ be the ordinary deformation ring and let $H^2_{\mathcal P_{\mathrm{ord}}}(\operatorname{Gal}_{\mathbb Q,\Sigma},\operatorname{Lie}\check{\mathrm G})$ denote the obstruction group for the ordinary deformation problem. Smoothness conjecture. If

$$H^2_{\mathcal P_{\mathrm{ord}}}(\operatorname{Gal}_{\mathbb Q,\Sigma},\operatorname{Lie}\check{\mathrm G})=0,$$

then $R_\rho^{\mathrm{ord}}$ is smooth of dimension $r-l_0$. This is described as a higher analogue of Leopoldt's conjecture and is used to obtain a sufficiently large derived Hecke action. The source presents the implication as the expected smoothness statement, with its justification supplied later.