Do baryons trace dark matter in the early universe?
Grin, Daniel (Institute for Advanced Study)

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 the baryonic and dark matter components, 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. At linear order in the usual line-of-sight formalism, these compensated isocurvature (CI) perturbations leave no imprint on the CMB at observable scales. Big-bang nucleosynthesis and galaxy cluster constraints allow the amplitudes of CI perturbations to be as large as $\sim10\%$. Here it is shown that CI fluctuations actually induce off-diagonal correlations between temperature/polarization spherical-harmonic coefficients, and cause additional B-mode polarization of the CMB, once higher order terms are accounted for. Using these correlations, it is in principle possible to detect CI perturbations and reconstruct the power spectrum of spatial fluctuations in the ratio of baryon and dark matter number densities, at the CMB surface of last scattering. We calculate the magnitude of these correlations, show how they may be measured, and estimate the sensitivity of ongoing and future experiments to these fluctuations. We find that Planck, ACT, SPT, and Polarbear are sensitive to fluctuations with amplitude $\sim 1\%$, while SPTPol, ACTPol, and future space-based polarization methods will probe amplitudes as low as $\sim 0.1\%$.