Large-amplitude isothermal fluctuations and high-density dark-matter clumps

Large-amplitude isothermal fluctuations in the dark matter energy density, parameterized by $\mathrm{\Phi }\equiv \delta \text{rhodm}\mathrm{/}\text{rhodm}$, are studied within the framework of a spherical collapse model. For $\mathrm{\Phi }\text{ga}1$, a fluctuation collapses in the radiation-dominated epoch and produces a dense dark-matter object. The final density of the virialized object is found to be $\rho_F \approx 140, \Phi^3 (\Phi+1) \rhoeq$,where$\rhoeq$ is the matter density at equal matter and radiation energy density. This expression is valid for the entire range of possible values of $\mathrm{\Phi }$, both for $\mathrm{\Phi }\gg 1$ and $\Phi \ll 1$. Some astrophysical consequences of high-density dark-matter clumps are discussed.