Power spectra based plank constraints on compensated isocurvature, and forwcasts for LiteBIRD and CORE space mission

Compensated isocurvature perturbations (CIP), where the primordial baryon and cold dark matter density perturbations cancel, do not cause total matter isocurvature perturbation. Consequently, at the linear order in the baryon density contrast Delta, a mixture of CIP and the adiabatic mode leads to the same CMB spectra as the pure adiabatic mode. Only recently, Munoz et al. showed that at the second order CIP leaves an imprint in the observable CMB by smoothing the power spectra in a similar manner as lensing. This causes a strong degeneracy between the CIP variance Delta(2)(rms) and the phenomenological lensing parameter A(L). We study several combinations of the Planck 2015 data and show that the measured lensing potential power spectrum C-l(phi phi) breaks the degeneracy. Nested sampling of the Lambda CDM+ Delta(rms) (2) (+ A(L)) model using the Planck 2015 temperature, polarization, and lensing data gives Delta(2)(rms) = (6.9(-3.1)(+3.0)) x 10(-3) at 68% CL. A non-zero value is favoured at 2.3 sigma (or without the polarization data at 2.8 sigma). CIP with Delta(2)(rms) approximate to 7 x 10(-3) improves the bestfit x(2) by 3.6 compared to the adiabatic Lambda CDM model. In contrast, although the temperature data favour A(L) similar or equal to 1.22, allowing A(L) not equal 1 does not improve the joint fi t at all, since the lensing data disfavour A(L) not equal 1. Indeed, CIP provides a rare example of a simple model, which is capable of reducing the Planck lensing anomaly significantly andfitting well simultaneously the high (and low) multipole temperature and lensing data, as well as the polarization data. Finally, we derive forecasts for two future satellite missions (LiteBIRD proposal to JAXA/NASA and Exploring Cosmic Origins with CORE proposal to ESA's M5 call) and compare these to simulated Planck data. Due to its coarse angular resolution, LiteBIRD is not able to improve the constraints on Delta(2)(rms) or A(L), but CORE-M5 (almost) reaches the cosmic variance limit and improves the CIP constraint to Delta(2)(rms) < 0.6 (1.4) x 10(-3) at 68 (95)% CL, which is nine times better than the current trispectrum based upper bound and six times better than obtained from the simulated Planck data. In addition, CORE-M5 will exquisitely distinguish between Delta(2)(rms) and A(L). No matter whether CIP is allowed for or not, the uncertainty of the lensing parameter will be sigma(A(L)) approximate to 0.012, in the case where the simulated data are based on the adiabatic Lambda CDM model with A(L) = 1.