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We propose an alternative scenario for the dark matter generation from an evolving cosmological constant which interacts with the dominant background in certain intermediate phase of the universe, and relaxes to the observed small value at present. In this way, it is shown that the interaction of the cosmological constant with the radiation or matter might generate the dark matter densities with a varied mass spectrum in the universe with their characteristic arc-like frozen signatures on the Cosmic Microwave Background Radiation (CMBR). This approach also suggests a possible solution to the long standing cosmological constant problem.

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