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We perform a joint analysis of the power spectrum and the bispectrum of theCMB temperature and polarization anisotropies to improve the constraints onisocurvature modes. We construct joint likelihoods, both for the existingPlanck data, and to make forecasts for the future LiteBIRD and CMB-S4experiments. We assume a general two-field inflation model with five freeparameters, leading to one isocurvature mode (which can be CDM density,neutrino density or neutrino velocity) arbitrarily correlated with theadiabatic mode. We theoretically assess in which cases (of detecting and/orfixing parameters) improvements can be expected, to guide our subsequentnumerical analyses. We find that for Planck, which detected neitherisocurvature modes nor primordial non-Gaussianity, the joint analysis does notimprove the constraints in the general case. However, if we fix additionalparameters in the model, the improvements can be highly significant dependingon the chosen parameter values. For LiteBIRD+CMB-S4 we study in which regionsof parameter space compatible with the Planck results the joint analysis willimprove the constraints or the significance of a detection. We find that, whilefor CDM isocurvature this region is very small, for the neutrino isocurvaturemodes it is much larger. In particular for neutrino velocity it can be abouthalf of the Planck-allowed region, where the joint analysis reduces theisocurvature error bars by up to 70%. In addition the joint analysis can alsoimprove the error bars of some of the standard cosmological parameters, by upto 30% for $\theta_{MC}$ for example, by breaking the degeneracies with thecorrelation parameter between adiabatic and isocurvature modes.

Isocurvature modes: joint analysis of the CMB power spectrum and bispectrum