CMB-S4: Forecasting Constraints on $f_{\mathrm{NL}}$ Through $\hat{I}¼$-distortion Anisotropy

Abstract

Diffusion damping of the cosmic microwave background (CMB) power spectrum results from imperfect photon-baryon coupling in the pre-recombination plasma. At redshift $5\times 10^4<z<2\times 10^6$, the plasma acquires an effective chemical potential, and energy injections from acoustic damping in this era create $\hat{I}¼$-type spectral distortions of the CMB. These $\hat{I}¼$ distortions trace the underlying photon density fluctuations, probing the primordial power spectrum in short-wavelength modes $k_{\mathrm{S}}$ over the range $50{\mathrm{Mpc}}^{-1}\lesssim k\lesssim 10^4{\mathrm{Mpc}}^{-1}$. Small-scale power modulated by long-wavelength modes $k_{\mathrm{L}}$ from squeezed-limit non-Gaussianities introduces cross-correlations between CMB temperature anisotropies and $\hat{I}¼$ distortions. Under single-field inflation models, $\hat{I}¼\times T$ correlations measured from an observer in an inertial frame should vanish up to a factor of $(k_{\mathrm{L}}/k_{\mathrm{S}}{)}^2\ll 1$. 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, parameterized by $f_{\mathrm{NL}}$, using measurements of $C_{\ell }^{\hat{I}¼T}$ as well as $C_{\ell }^{\hat{I}¼E}$ from CMB $E$ modes. Using current experimental specifications and foreground modeling, we expect $\ddot{I}ƒ(f_{\mathrm{NL}})\lesssim 1000$. This is roughly four times better than the current limit on $f_{\mathrm{NL}}$ using $\hat{I}¼\times T$ and $\hat{I}¼\times E$ 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 $k\simeq 740{\text{Mpc}}^{-1}$ and is thus highly complementary to measurements at larger scales from primary CMB and large-scale structure.

19 pages, 6 figures