  A novel class of integrable $\sigma$-models interpolating between exact coset
conformal field theories in the IR and hyperbolic spaces in the UV is
constructed. We demonstrate the relation to the asymptotic limit of
$\lambda$-deformed models for cosets of non-compact groups. An integrable model
interpolating between two spacetimes with cosmological and black hole
interpretations and exact conformal field theory descriptions is also provided.
In the process of our work, a new zoom-in limit, distinct from the well known
non-Abelian T-duality limit, is found.
