Measuring the Hubble constant from the cooling of the CMB monopole

TL;DR

This paper proposes a method to measure the Hubble constant by observing the cooling of the CMB monopole over time, offering a potentially independent way to address the Hubble tension.

Contribution

It forecasts the precision of measuring the Hubble constant through CMB spectral observations, highlighting the feasibility and challenges of this novel approach.

Findings

A 3000-bin spectrometer could measure H0 to 3% accuracy in 10 years.

Foreground separation is the main challenge for this method.

High-precision spectral distortion measurements are possible with future technology.

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. 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.