Cosmologies including continuous matter creation are able to reproduce the main properties of the standard ΛCDM model, in particular in cases where the particle and entropy production rates are equal. These specific models, characterized by a mass density equal to the critical value, behave like the standard ΛCDM model at early times whereas their late evolution is similar to the steady-state cosmology. The maximum amplitude of density fluctuations in these models depends on the adopted creation rate, related here to the parameter v and this limitation could be a difficulty for the formation of galaxies and large-scale structure in this class of universe. Additional problems are related with predictions either of the random peculiar velocities of galaxies or the present density of massive clusters of galaxies, both being largely overestimated with respect to observational data.

A massive gravity theory was proposed by Visser in the late nineties. This theory, based on a backgroung metric b αβ and on an usual dynamical metric g αβ has the advantage of being free of ghosts as well as discontinuities present in other massive theories proposed in the past. In the present investigation, the equations of Visser's theory are revisited with a particular care on the related conservation laws. It will be shown that a multiplicative factor is missing in the graviton tensor originally derived by Visser, which has no incidence on the weak field approach but becomes important in the strong field regime when, for instance, cosmological applications are considered. In this case, contrary to some previous claims found in the literature, we conclude that a non-static background metric is required in order to obtain a solution able to mimic the ΛCDM cosmology.

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