CMB-S4 forecasts for constraints on f_NL through -distortion anisotropy

Diffusion damping of the cosmic microwave background (CMB) power spectrum results from imperfect photon-baryon coupling in the pre-recombination plasma. Energy release at redshifts 5 x 10(4) < z < 2 x 10(6) can create mu-type spectral distortions of the CMB. These mu distortions trace the underlying photon density fluctuations, probing the primordial power spectrum in short-wavelength modes k(S) over the range 50 Mpc(-1) less than or similar to k less than or similar to 10(4) Mpc(-1). Small-scale power modulated by long-wavelength modes k(L) from squeezed limit non-Gaussianities introduces cross correlations between CMB temperature anisotropies and pi distortions. Under single-field inflation models, mu x T correlations measured from an observer in an inertial frame should vanish up to a factor of (k(L)/k(S))(2) << 1. Thus, any measurable correlation rules out single-field inflation models. We forecast how well the next-generation ground-based CMB experiment CMB-S4 will be able to constrain primordial squeezed-limit non-Gaussianity, parametrized by f(NL), using measurements of C-l(mu T) as well as C-l(mu E) from CMB E modes. Using current experimental specifications and foreground modeling, we expect sigma(f(NL)) less than or similar to 1000. This is roughly 4 times better than the current limit on f(NL) using mu x T and mu x E correlations from Planck and is comparable to what is achievable with LiteBIRD, demonstrating the power of the CMB-S4 experiment. This measurement is at an effective scale of k approximate to 740 Mpc(-1) and is thus highly complementary to measurements at larger scales from primary CMB and large-scale structure.