Working with Duncan Hanson,we used the WMAP 9-year maps to search for evidence of compensated isocurvature perturbations (CIPs) using the techniques outlined in arXiv:1107.5047. We find that baryons do trace dark matter at the ~10% level (expressed as a limit on the CIP amplitude).
Unlike isocurvature perturbations between photons and neutrinos, CDM, or baryons, isocurvature perturbations between dark matter and baryons are surprisingly poorly constrained. A cartoon of such a perturbation is shown in the cartoon above. This is because they don’t induce an early-time radiation pressure gradient, or a gravitational potential perturbation. Although they do induce a baryonic pressure perturbation, this is not active on the scales we can directly access in the CMB. In arXiv:1107.5047, my collaborators and I showed that these compensated isocurvature perturbations (CIPs) do have observable effects on the CMB due to higher-order effects that induce off-diagonal correlations in the CMB, essentially by spatially modulating the baryon-photon sound speed before hydrogen recombination. Here, we used Monte-Carlo simulations and corrected our estimator for fractional sky coverage. We then searched the WMAP 9-year maps for evidence of CIPs. We check that non-Gaussian reconstruction noise and bias are negligible for the purposes of WMAP-based searches for CIPs. We found no evidence for CIPs, and our final results are shown in the figure below, which shows the 95-% confidence-level upper limit to the rms CIP amplitude as a ‘ of angular scale.