Do baryons trace dark matter in the early universe?

Baryon-density perturbations of large amplitude may exist if they are compensated by dark-matter perturbations so that the total density remains unchanged. Big-bang nucleosynthesis and galaxy clusters allow the amplitudes of these compensated isocurvature perturbations (CIPs) to be as large as $\sim10%$. CIPs will modulate the power spectrum of cosmic microwave background (CMB) fluctuations---those due to the usual adiabatic perturbations---as a function of position on the sky. This leads to correlations between different spherical-harmonic coefficients of the temperature/polarization map, and it induces B modes in the CMB polarization. Here, the magnitude of these effects is calculated and techniques to measure them are introduced. While a CIP of this amplitude can be probed on the largest scales with WMAP, forthcoming CMB experiments should improve the sensitivity to CIPs by at least an order of magnitude.