The Warm Dark Matter plus Baryon Linear Power Spectrum

We study linear density perturbations in an extension of Newtonian cosmology. The extension includes warm dark matter and baryons. The effect of the warm dark matter particle thermal velocity is to prevent short wavelength perturbations from growing. We obtain the linear power spectrum relative to cold dark matter, prior to galaxy formation, for warm dark matter with a Maxwell or Bose-Einstein thermal velocity distribution. This prediction can be tested with precision weak gravitational lensing observations of the cosmic microwave background radiation.