  In this paper we prove global well-posedness and scattering for the
defocusing cubic nonlinear wave equation in the hyperbolic space
$\mathbb{H}^3$, under the assumption that the initial data is radial and lies
in $H^{\frac{1}{2}+\delta}(\mathbb{H}^3)\times
H^{-\frac{1}{2}+\delta}(\mathbb{H}^3)$
