What Mass Are the Smallest Protohalos?

We calculate the kinetic-decoupling temperature for weakly interacting massive particles (WIMPs) in supersymmetric (SUSY) and extra dimensional models that can account for the cold-dark-matter abundance determined from cosmic microwave background measurements. Depending on the parameters of the particle-physics model, a wide variety of decoupling temperatures is possible, ranging from several MeV to a few GeV. These decoupling temperatures imply a range of masses for the smallest protohalos much larger than previously thought—ranging from ${10}^{-6}{M}_{\oplus }$ to ${10}^2{M}_{\oplus }$. We expect the range of protohalos masses derived here to be characteristic of most particle-physics models that can thermally accommodate the required relic abundance of WIMP dark matter, even beyond SUSY and extra dimensions.