Measurements of cosmic microwave background (CMB) anisotropies constrain isocurvature fluctuations between photons and non-relativistic particles to be sub-dominant to adiabatic fluctuations. Perturbations in the relative number densities of baryons and dark matter, however, are surprisingly poorly constrained. In fact, baryon-density perturbations of fairly large amplitude may exist if they are compensated by dark-matter perturbations, so that the total density remains unchanged. These compensated isocurvature perturbations (CIPs) leave no imprint on the CMB at observable scales, at linear order in their amplitude. I will review the standard lore on isocurvature, and motivate the consideration of CIPs. I will then consider a variety of astrophysical probes of CIPs. I will then show that the conventional wisdom on CIPs fails: CIPs do leave an imprint on the cosmic microwave background, providing a new mode for B-mode generation. I will show how the cosmic microwave background could be used to probe for fluctuations between baryon and dark matter. I will conclude by considering both some practical issues involved in CIP extraction from the data, and horizons for future theoretical work on CIPs.
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