We investigate the cosmology of interacting spin-2 particles, formulating themulti-gravitational theory in terms of vierbeins and without imposing anyDeser-van Nieuwenhuizen-like constraint. The resulting multi-vierbein theoryrepresents a wider class of gravitational theories if compared to thecorresponding multi-metric models. Moreover, as opposed to its metriccounterpart which in general seems to contain ghosts, it has already beenproved to be ghost-free. We outline a discussion about the possible mattercouplings and we focus on the study of cosmological scenarios in the case ofthree and four interacting vierbeins. We find rich behavior, including deSitter solutions with an effective cosmological constant arising from themulti-vierbein interaction, dark-energy solutions and nonsingular bouncingsolutions.
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