  Although both early and late-time modifications of the $\Lambda$CDM model
have been proposed to address the Hubble tension, compelling arguments suggest
that for a solution to be successful it needs to modify the expansion history
of the universe prior to recombination. This greatly increases the importance
of precise CMB observations, and in this letter we make the argument for CMB
spectral distortions, highlighting their potential role in constraining models
that introduce significant shifts in the standard $\Lambda$CDM parameters, such
as the scalar spectral index, in attempt to solve the Hubble tension.
