The property (T) rank-gradient conjecture

Let $\Gamma$ be an infinite group with Kazhdan property (T), and let $(\Gamma_n)$ be a normal chain in $\Gamma$ with trivial intersection. Write $\mathrm{RG}(\Gamma,(\Gamma_n))$ for the rank gradient of $\Gamma$ with respect to this chain. Property (T) rank-gradient conjecture.

$$\mathrm{RG}(\Gamma,(\Gamma_n))=0.$$

The conjecture concerns the cases where property (T) forces the first $L^2$ Betti number to vanish, but it was not known in the source whether the rank gradient must also vanish.