The power spectrum of SUSY-CDM on subgalactic scales

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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