Measuring the Hubble constant from the cooling of the CMB monopole
  The cosmic microwave background (CMB) monopole temperature evolves with the
inverse of the cosmological scale factor, independent of many cosmological
assumptions. With sufficient sensitivity, real-time cosmological observations
could thus be used to measure the local expansion rate of the Universe using
the cooling of the CMB. We forecast how well a CMB spectrometer could determine
the Hubble constant via this method. The primary challenge of such a mission
lies in the separation of Galactic and extra-Galactic foreground signals from
the CMB at extremely high precision. However, overcoming these obstacles could
potentially provide an independent, highly robust method to shed light on the
current low-/high-$z$ Hubble tension. An experiment with 3000 linearly spaced
bins between 5 GHz and 3 THz with a sensitivity of 1
$\mathrm{mJy\sqrt{yr}~sr^{-1}}$ per bin, could measure $H_0$ to 3% over a 10
year mission, given current foreground complexity. This sensitivity would also
enable high-precision measurements of the expected $\Lambda$CDM spectral
distortions, but remains futuristic at this stage.
