CMB-S4 forecasts for constraints on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>NL</mml:mi></mml:mrow></mml:msub></mml:math> through <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi></mml:math>-distortion anisotropy

Abstract

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 $5\ifmmode\times\else\texttimes\fi{}{10}^{4}&lt;z&lt;2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ can create $\ensuremath{\mu}$-type spectral distortions of the CMB. These $\ensuremath{\mu}$ distortions trace the underlying photon density fluctuations, probing the primordial power spectrum in short-wavelength modes ${k}_{\mathrm{S}}$ over the range $50\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}\ensuremath{\lesssim}k\ensuremath{\lesssim}{10}^{4}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. Small-scale power modulated by long-wavelength modes ${k}_{\mathrm{L}}$ from squeezed-limit non-Gaussianities introduces cross correlations between CMB temperature anisotropies and $\ensuremath{\mu}$ distortions. Under single-field inflation models, $\ensuremath{\mu}\ifmmode\times\else\texttimes\fi{}T$ correlations measured from an observer in an inertial frame should vanish up to a factor of $({k}_{\mathrm{L}}/{k}_{\mathrm{S}}{)}^{2}\ensuremath{\ll}1$. 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, parametrized by ${f}_{\mathrm{NL}}$, using measurements of ${C}_{\ensuremath{\ell}}^{\ensuremath{\mu}T}$ as well as ${C}_{\ensuremath{\ell}}^{\ensuremath{\mu}E}$ from CMB $E$ modes. Using current experimental specifications and foreground modeling, we expect $\ensuremath{\sigma}({f}_{\mathrm{NL}})\ensuremath{\lesssim}1000$. This is roughly 4 times better than the current limit on ${f}_{\mathrm{NL}}$ using $\ensuremath{\mu}\ifmmode\times\else\texttimes\fi{}T$ and $\ensuremath{\mu}\ifmmode\times\else\texttimes\fi{}E$ 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 $k\ensuremath{\approx}740\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ and is thus highly complementary to measurements at larger scales from primary CMB and large-scale structure.

Topics & Concepts