Abstract

ABSTRACT The formation of large scale structure is independent of the nature of the cold darkmatter (CDM), however the fate of very small scale inhomogeneities depends on themicro-physics of the CDM particles. We investigate the matter power spectrum forscales that enter the Hubble radius well before matter-radiation equality, and followits evolution until the time when the first inhomogeneities become non-linear. Ourfocus lies on weakly interacting massive particles (WIMPs), and as a concrete exam-ple we analyze the case when the lightest supersymmetric particle is a bino. We showthat collisional damping and free-streaming of WIMPs lead to a matter power spec-trum with a sharp cut-off at about 10 −6 M ⊙ and a maximum close to that cut-off. Wealso calculate the transfer function for the growth of the inhomogeneities in the lin-ear regime. These three effects (collisional damping, free-streaming and gravitationalgrowth) are combined to provide a WMAP normalized primordial CDM power spec-trum, which could serve as an input for high resolution CDM simulations. The smallestinhomogeneities typically enter the non-linear regime at a redshift of about 60.Key words: cosmology: theory – dark matter – early Universe

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