Cosmology with Rayleigh scattering of the cosmic microwave background

The cosmic microwave background (CMB) has been a treasure trove for cosmology. Over the next decade, current and planned CMB experiments are expected to exhaust nearly all primary CMB information. To further constrain cosmological models, there is a great benefit to measuring signals beyond the primary modes. Rayleigh scattering of the CMB is one source of additional cosmological information. It is caused by the additional scattering of CMB photons by neutral species formed during recombination and exhibits a strong and unique frequency scaling ($\propto \nu^4$). We will show that with sufficient sensitivity across frequency channels, the Rayleigh scattering signal should not only be detectable but can significantly improve constraining power for cosmological parameters, with limited or no additional modifications to planned experiments. We will provide heuristic explanations for why certain cosmological parameters benefit from measurement of the Rayleigh scattering signal, and confirm these intuitions using the Fisher formalism. In particular, observation of Rayleigh scattering allows significant improvements on measurements of $N_{\rm eff}$ and $\sum m_\nu$.