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

Large-amplitude isothermal fluctuations in the dark-matter energy density, parametrized by Φ≡δ${\mathrm{\rho }}_{\mathrm{DM}}$/${\mathrm{\rho }}_{\mathrm{DM}}$, are studied within the framework of a spherical collapse model. For Φ≳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 ${\mathrm{\rho }}_{\mathit{F}}$≊140${\mathrm{\Phi }}^3$(Φ+1)${\mathrm{\rho }}_{\mathrm{eq}}$, where ${\mathrm{\rho }}_{\mathrm{eq}}$ is the matter density at equal matter and radiation energy density. This expression is valid for the entire range of possible values of Φ, both for Φ≫1 and Φ≪1. Some astrophysical consequences of high-density dark-matter clumps are discussed.