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We develop a model of production of the very dense clumps of DM in RD epochdue to the accretion of DM on the loops of cosmic strings as the seeds. At sometime the loops disappear, for example due to the gravitational radiation, andthe remaining dense clumps produce the enhancement of the annihilation signal.We take into account the velocity distribution of the strings, and consider thetwo extreme regimes of DM annihilation: fast decay and continuous evaporation.The produced annihilation flux of gamma radiation is detectable, and for someparameters of DM particles and the strings can exceed the extragalactic flux ofthe gamma-radiation observed by Fermi. For the fixed parameters of DM particles(e.g. neutralino with fixed masses and cross-section of annihilation) one canobtain the limits on the basic string parameter, tension \mu, which is strongerthan (more general) limits obtained from WMAP observations, cosmologicalnucleosynthesis and gravitational lensing. In particular for the neutralinowith 100 GeV mass we exclude the interval5\times10^{-10}<G{\mu}/c^2<5.1\times10^{-9}.

Dense DM clumps seeded by cosmic string loops and DM annihilation