One interesting feature of compensated isocurvature perturbations (CIPs) is that they have a similar effect on CMB power spectra to weak lensing of the CMB. CIPs are fluctuations in the relative number densities of dark matter and baryons. In this work (led by Johns Hopkins graduate student Julian B. Muñoz under my mentorship & supervised by Marc Kamionkowski), we used a new mathematically & simple formulation to compute the effect of CIPs on the CMB power spectrum, derive new limits (competitive with WMAP limits from off-diagonal correlations obtained by D. Hanson and me), and showed how CIPs might help resolve the discrepancy between the observed level of CMB lensing in Planck power spectra and theory. We also found a new limit to the root-mean-squared fluctuation associated with a scale-invariant spectrum of CIPs, .
Result on the arXiv (under review by Phys. Rev. D): arXiv:1511.04441.
The figure below shows the logarithmic derivative of the CMB temperature power spectrum with respect to and standard cosmological parameters. We see that CIPs are nearly degenerate with deviations from the lensing amplitude .