We report on the current construction status of the IceCube high energy neutrino observatory and possible future construction plans. With the completion of the fourth construction season in Feb. 2008, the observatory is now instrumenting half a cubic kilometer of ice, greatly increasing the horizon for high energy neutrino detection. We briefly describe physics topics related to cosmology, such as indirect searches for supersymmetric cold dark matter, for slow and relativistic magnetic monopoles, GZK neutrinos and violation of Lorentz invariance or Equivalence Principle. It is anticipated that upon completion the new detector will vastly increase the sensitivity and extend the reach of AMANDA to higher energies.