Various cosmological observations tell us that about 24% of the total energy density of the universe exists in the form of nonrelativistic dark matter. But they fail to provide any information about the epoch or method of formation of the dark matter. There are particle physics models where the cold dark matter is formed late after a phase transition during the history of the universe. A model independent way to probe these models is to study their cosmological aspects. We shall try to compute the matter power spectrum of this delayed dark matter model and discuss the new effects originating due to the late formation of cold dark matter. We shall also try to identify the nature of the dark sector prior to the phase transition from its imprints on the matter power spectrum.