An Uncountable Family of Non Orbit Equivalent Actions of ${\mathbb{F}}_n$

For each $2\le n\le \mathrm{\infty }$, we construct an uncountable family of free ergodic measure preserving actions ${\alpha }_t$ of the free group ${\mathbb{F}}_n$ on the standard probability space $(X,\mu )$ such that any two are non orbit equivalent (in fact, not even stably orbit equivalent). These actions are all ``rigid’’ (in the sense of [Po01]), with the II${}_1$ factors $L^\infty(X, \mu)\rtimes_{\alpha_t} \Bbb F_n$ mutually non stably isomorphic (even non-stably isomorphic) and in the class $\text{Cal}H\text{Cal}{T}_{{}_s}\mathrm{.}$