Compensated Isocurvature Perturbations and the Cosmic Microwave
  Background
  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. B modes in the CMB polarization are generated at reionization
through the modulation of the optical depth by CIPs, but this induced
polarization is small. The strongest known constraint $\lesssim 10%$ to the CIP
amplitude comes from galaxy cluster baryon fractions. Here it is shown that
modulation of the baryon density by the CIP at and before the decoupling of
Thomson scattering at $z\sim 1100$ gives rise to CMB effects several orders of
magnitude larger than those considered before. Polarization B modes are
induced, as are correlations between temperature/polarization
spherical-harmonic coefficients of different $lm$. It is shown that the CIP
field at the surface of last scatter can be measured with these higher-order
correlations. The sensitivity of ongoing and future experiments to these
fluctuations is estimated. Data from the WMAP, ACT, SPT, and Spider experiments
will be sensitive to fluctuations with amplitude $\sim 5-10%$. The Planck
satellite and Polarbear experiment will be sensitive to fluctuations with
amplitude $\sim 3%$. SPTPol, ACTPol, and future space-based polarization
methods will probe amplitudes as low as $\sim 0.4%-0.6%$. In the cosmic
variance limit, the lowest amplitude CIPs that could be detected with the CMB
are of amplitude $\sim 0.05%$.
