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Leverage on small-scale primordial non-Gaussianity through cross-correlations between CMB $E$-mode and $μ$-distortion anisotropies

Multi-field inflation models and non-Bunch-Davies vacuum initial conditions both predict sizeable non-Gaussian primordial perturbations and anisotropic $μ$-type spectral distortions of the cosmic microwave background (CMB) blackbody. While CMB anisotropies allow us to probe non-Gaussianity at wavenumbers $k\simeq 0.05\,{\rm Mpc^{-1}}$, $μ$-distortion anisotropies are related to non-Gaussianity of primordial perturbation modes with much larger wavenumbers, $k\simeq 740\,{\rm Mpc^{-1}}$. Through cross-correlations between CMB and $μ$-distortion anisotropies, one can therefore shed light on the aforementioned inflation models. We investigate the ability of a future CMB satellite imager like LiteBIRD to measure $μT$ and $μE$ cross-power spectra between anisotropic $μ$-distortions and CMB temperature and $E$-mode polarization anisotropies in the presence of foregrounds, and derive LiteBIRD forecasts on ${f_{\rm NL}^μ(k\simeq 740\,{\rm Mpc^{-1}})}$. We show that $μE$ cross-correlations with CMB polarization provide more constraining power on $f_{\rm NL}^μ$ than $μT$ cross-correlations in the presence of foregrounds, and the joint combination of $μT$ and $μE$ observables adds further leverage to the detection of small-scale primordial non-Gaussianity. We find that LiteBIRD would detect ${f_{\rm NL}^μ}=4500$ at $5σ$ significance after foreground removal, and achieve a minimum error of ${σ(f_{\rm NL}^μ=0) \simeq 800}$ at 68\% CL by combining CMB temperature and polarization. Due to the huge dynamic range of wavenumbers between CMB and $μ$-distortion anisotropies, such large $f^μ_{\rm NL}$ values would still be consistent with current CMB constraints in the case of very mild scale-dependence of primordial non-Gaussianity. Anisotropic spectral distortions thus provide a new path, complementary to CMB $B$-modes, to probe inflation with LiteBIRD.