Measuring the Duration of Last Scattering

The cosmic microwave background (CMB) fluctuations effectively measure the basic properties of the universe during the recombination epoch. CMB measurements fix the distance to the surface of last scatter, the sound horizon of the baryon-photon fluid and the fraction of the energy density in relativistic species. We show that the microwave background observations can also very effectively constrain the thickness of the last scattering surface, which is directly related to the ratio of the small-scale E-mode polarization signal to the small-scale temperature signal. The current cosmological data enables a 0.1\% measurement of the thickness of the surface of last scatter: $19 \pm 0.065$ Mpc. This constraint is relatively model-independent, so it can provide a new metric for systematic errors and an independent test of the $\Lambda {\rm CDM}$ model. On the other hand, it is sensitive to models which affect the reionization history of the universe such as models with annihilating dark matter and varying fundamental constants (e.g., the fine-structure constant, $\alpha_{\rm EM}$, and electron rest mass, $m_{\rm e}$) and as such can be used as a viable tool to constrain them.