  Recently, evidence has been collected that a class of gravitational theories
with certain non-local operators is renormalizable. We consider one such model
which, at the linear perturbative level, reproduces the effective non-local
action for the light modes of bosonic closed string-field theory. Using the
property of asymptotic freedom in the ultraviolet and fixing the classical
behavior of the scale factor at late times, an algorithm is proposed to find
general homogeneous cosmological solutions valid both at early and late times.
Imposing a power-law classical limit, these solutions (including anisotropic
ones) display a bounce, instead of a big-bang singularity, and super-accelerate
near the bounce even in the absence of an inflaton or phantom field.
