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

Primordial isocurvature fluctuations between photons and either neutrinos or nonrelativistic species such as baryons or dark matter are known to be subdominant to adiabatic fluctuations. Perturbations in the relative densities of baryons and dark matter (known as compensated isocurvature perturbations or CIPs), however, are surprisingly poorly constrained. CIPs leave no imprint in the cosmic microwave background (CMB) on observable scales, at least at linear order in their amplitude and zeroth order in the amplitude of adiabatic perturbations. It is thus not yet empirically known if baryons trace dark matter at the surface of last scattering. If CIPs exist, they would spatially modulate the Silk damping scale and acoustic horizon, causing distinct fluctuations 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 used to conduct the first CMB-based observational search for CIPs, using off-diagonal correlations and the CMB trispectrum. Reconstruction noise from weak lensing and point sources is shown to be negligible for this data set. No evidence for CIPs is observed, and a 95% confidence upper limit of 1.1×10^-2 is imposed to the amplitude of a scale-invariant CIP power spectrum. This limit agrees with CIP sensitivity forecasts for WMAP and is competitive with smaller-scale constraints from measurements of the baryon fraction in galaxy clusters. It is shown that the root-mean-squared CIP amplitude on 5-100 scales is smaller than ∼0.07-0.17 (depending on the scale) at the 95% confidence level. Temperature data from the Planck satellite will provide an even more sensitive probe for the existence of CIPs, as will the upcoming ACTPol and SPTPol experiments on smaller angular scales.