  An analytic approach to phenomenological models inspired by cubic string
field theory is introduced and applied to some examples. We study a class of
actions for a minimally coupled, homogeneous scalar field whose energy density
contains infinitely many time derivatives. These nonlocal systems are
systematically localized and an algorithm to find cosmological solutions of the
dynamical equations is provided. Our formalism is able to define the nonlocal
field in regions of the parameter space which are inaccessible by standard
methods. Also, problems related to nonlocality are reinterpreted under a novel
perspective and naturally overcome. We consider phenomenological models living
on a Friedmann-Robertson-Walker background with power-law scale factor, both in
four dimensions and on a high-energy braneworld. The quest for solutions
unravels general features of nonlocal dynamics indicating several future
directions of investigation.
