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Primordial isocurvature fluctuations between photons and either neutrinos ornon-relativistic species such as baryons or dark matter are known to besub-dominant to adiabatic fluctuations. Perturbations in the relative densitiesof baryons and dark matter (known as compensated isocurvature perturbations, orCIPs), however, are surprisingly poorly constrained. CIPs leave no imprint inthe cosmic microwave background (CMB) on observable scales, at least at linearorder in their amplitude and zeroth order in the amplitude of adiabaticperturbations. It is thus not yet empirically known if baryons trace darkmatter at the surface of last scattering. If CIPs exist, they would spatiallymodulate the Silk damping scale and acoustic horizon, causing distinctfluctuations in the CMB temperature/polarization power spectra across the sky:this effect is first order in both the CIP and adiabatic mode amplitudes. Here,temperature data from the Wilkinson Microwave Anisotropy Probe (WMAP) are usedto conduct the first CMB-based observational search for CIPs, usingoff-diagonal correlations and the CMB trispectrum. Reconstruction noise fromweak lensing and point sources is shown to be negligible for this data set. Noevidence for CIPs is observed, and a 95%-confidence upper limit of $1.1\times10^{-2}$ is imposed to the amplitude of a scale-invariant CIP power spectrum.This limit agrees with CIP sensitivity forecasts for WMAP, and is competitivewith smaller scale constraints from measurements of the baryon fraction ingalaxy clusters. It is shown that the root-mean-squared CIP amplitude on 5-100degree scales is smaller than 0.07-0.17 (depending on the scale) at the95%-confidence level. Temperature data from the Planck satellite will providean even more sensitive probe for the existence of CIPs, as will the upcomingACTPol and SPTPol experiments on smaller angular scales.

Baryons do trace dark matter 380,000 years after the big bang: Search for compensated isocurvature perturbations with WMAP 9-year data