Cold + Hot Dark Matter and the Cosmic Microwave Background

We examine the cosmic microwave background power spectrum for adiabatic models with a massive neutrino component. We present the results of a detailed numerical evolution of cold + hot dark matter (CHDM) models and compare with the standard cold dark matter (CDM) spectrum. The difference is of order $5-10%$ for $400 < l < 1000 $ for currently popular CHDM models. With semi-analytic approximations, we also discuss the relevant physics involved. Finally we remark on the ability of future experiments to differentiate between these models. An all-sky experiment with a beam size smaller than 30 arcminutes can distinguish between CHDM and CDM if other cosmological parameters are known. Even allowing other parameters to vary, it may be possible to distinguish CDM from CHDM.Comment: Compressed uuencoded postscript, 26 pages including figures. Color version available at http://www-astro-theory.fnal.gov