Mixed Inflaton and Spectator Field Models: CMB constraints and $\mu$ distortion

We discuss mixed inflaton and spectator field models where both the fields are responsible for the observed density fluctuations. We use the current CMB data to constrain both the general mixed model as well as some specific representative scenarios, and collate the results with the model predictions for the CMB spectral $\mu$ distortion. We find the posterior distribution of $\mu$ using MCMC chains and demonstrate that the standard single-field inflaton model typically predicts $\mu \sim 10^{-8}$ with a relatively narrow distribution, whereas for the mixed models, the distribution turns out to be much broader, and $\mu$ could be larger by almost an order of magnitude. Hence future experiments of $\mu$ distortion could provide a tool for the critical testing of the mixed source models of the primordial perturbation.