Secular evolution of galaxies and galaxy clusters in decaying dark matter cosmology

If the dark matter sector in the Universe is composed by metastable particles, galaxies and galaxy clusters are expected to undergo significant secular evolution from high to low redshift. We show that the decay of dark matter, with a lifetime compatible with cosmological constraints, can be at the origin of the observed evolution of the Tully-Fisher relation of disk galaxies and alleviate the problem of the size evolution of elliptical galaxies, while being consistent with the current observational constraints on the gas fraction of clusters of galaxies.