Let $\rho:\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})\rightarrow \operatorname{GL}_2(\bar{\mathbb{Z}}_p)$ be a $p$-adic Galois representation associated to a $p$-ordinary Hecke eigencuspform, let $\bar{\rho}:\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})\rightarrow \operatorname{GL}_2(\bar{\mathbb{F}}_p)$ denote the residual representation. The adjoint representation $\operatorname{Ad}\rho$ is the module of $2\times 2$ trace-zero matrices over $\bar{\mathbb{Q}}_p$ on which $\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ acts by conjugation. There is a relationship between the Selmer group over $\mathbb{Q}$ of the (characteristic zero) adjoint representation $\operatorname{Ad}\rho$ and a certain universal Galois deformation ring associated to $\bar{\rho}$. Namely, the dual of the adjoint Selmer group over $\mathbb{Q}$ is isomorphic to the module of $1$-forms on the deformation ring at the point corresponding to $\rho$. In the case when $\rho$ is unramified outside $p$, a proof of this statement is in Hida's book "Hilbert Modular forms and Iwasawa theory" (cf. Proposition 1.47). The relationship generalizes to totally real fields. The relationship here tells us that since the deformation ring comes from a Hecke algebra, then indeed the Selmer group of the Adjoint representation over $\mathbb{Q}$ is finite (cf. Proposition 1.53), and the same statement holds over a totally real field. This requires the hypothesis that $\rho$ is unramified outside $p$. A similar idea was exploited by Khare and Ramakrishna to show that if one starts with a residual Galois representation which is odd and absolutely irreducible then it may be lifted to a $p$-adic Galois representation for which the adjoint Selmer group is finite, this does not require the hypothesis that $\rho$ is unramified outside $p$.

My question is the following, can one use similar lines of reasoning to say anything about the structure of the adjoint Selmer group over the cyclotomic $\mathbb{Z}_p$ extension of $\mathbb{Q}$? Has this been explored anywhere?