  We consider cosmological models based on the spectral action formulation of
(modified) gravity. We analyze the coupled effects, in this model, of the
presence of nontrivial cosmic topology and of fractality in the large scale
structure of spacetime. We show that the topology constrains the possible
fractal structures, and in turn the correction terms to the spectral action due
to fractality distinguish the various cosmic topology candidates, with effects
detectable in a slow-roll inflation scenario, through the power spectra of the
scalar and tensor fluctuations. We also discuss explicit effects of the
presence of fractal structures on the gravitational waves equations.
