Unlike isocurvature perturbations between photons and neutrinos, CDM, or baryons, isocurvature perturbations between dark matter and baryons are surprisingly poorly constrained. In this work, we show that such perturbations do have observable effects on the CMB due to higher-order effects that induce off-diagonal correlations and non-Gaussianity in the CMB.
In linear theory, these `compensated isocurvature perturbations’ (or CIPs) source no radiation pressure gradients or potential perturbations, and the resulting baryonic pressure perturbations are relevant only on extremely small scales; this is why these modes are poorly constrained by the data. CIPs could be excited in the curvaton model. More plainly though, we only know that baryons trace dark matter spatially to a precision of 1-10% today with no primordial constraint, a much larger rms fluctuation than the 10 -5 fluctuations we are used to speaking of in CMB cosmology.
Prior work suggested that the only way to probe this possibility was using neutral 21-cm cosmology. We found, however, that at second order, spatial modulation of the diffusion and baryon acoustic scales would lead to detectable off-diagonal correlations in the CMB, allowing near-term improvement of sensitivity to CIP amplitudes of 0.1%, and 0.01% with ongoing/forthcoming CMB experiments like Planck, SPTPol, and ACTPol. We developed the statistical tools needed to extract this signal from the CMB.