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. We find that a 3% measurement of the Hubble constant requires an effective sensitivity to the CMB monopole temperature of approximately 60 pKpyr throughout a 10-year mission. This sensitivity would also enable high-precision measurements of the expected CDM spectral distortions, but remains futuristic at this stage.