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Search for Compensated Isocurvature Perturbations with Planck Power Spectra

In the standard inflationary scenario, primordial perturbations are adiabatic. The amplitudes of most types of isocurvature perturbations are generally constrained by current data to be small. If, however, there is a baryon-density perturbation that is compensated by a dark-matter perturbation in such a way that the total matter density is unperturbed, then this compensated isocurvature perturbation (CIP) has no observable consequence in the cosmic microwave background (CMB) at linear order in the CIP amplitude. Here we search for the effects of CIPs on CMB power spectra to quadratic order in the CIP amplitude. An analysis of the Planck temperature data leads to an upper bound $Δ_{\rm rms}^2 \leq 7.1\times 10^{-3}$, at the 68\% confidence level, to the variance $Δ_{\rm rms}^2$ of the CIP amplitude. This is then strengthened to $Δ_{\rm rms}^2\leq 5.0\times 10^{-3}$ if Planck small-angle polarization data are included. A cosmic-variance-limited CMB experiment could improve the $1σ$ sensitivity to CIPs to $Δ^2_{\rm rms} \lesssim 9\times 10^{-4}$. It is also found that adding CIPs to the standard $Λ$CDM model can improve the fit of the observed smoothing of CMB acoustic peaks just as much as adding a non-standard lensing amplitude.