Abstract
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 $60~pK \sqrtyr$ throughout a 10-year
mission. This sensitivity would also enable high-precision measurements of the
expected $Łambda$CDM spectral distortions, but remains futuristic at this
stage.
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