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Dark energy, matter creation and curvature

The most studied way to explain the current accelerated expansion of the universe is to assume the existence of dark energy; a new component that fill the universe, does not clumps, currently dominates the evolution, and has a negative pressure. In this work I study an alternative model proposed by Lima et al. \cite{lima96}, which does not need an exotic equation of state, but assumes instead the existence of gravitational particle creation. Because this model fits the supernova observations as well as the $Λ$CDM model, I perform in this work a thorough study of this model considering an explicit spatial curvature. I found that in this scenario we can alleviate the cosmic coincidence problem, basically showing that these two components, dark matter and dark energy, are of the same nature, but they act at different scales. I also shown the inadequacy of some particle creation models, and also I study a previously propose new model that overcome these difficulties.