Thomson scattering: One rate to rule them all

Understand

The enduring tension between local and distant measurements of $H_0$ remains unresolved.

• It was recently pointed out that cosmic microwave background (CMB) and large-scale structure (LSS) observables are invariant under a uniform rescaling of the gravitational free-fall rates of all species present and the Thomson scattering rate between photons and electrons.
• We show that a unique variation of the fine-structure constant $\alpha$ and the electron mass $m_{\rm e}$ can leverage this scaling transformation to reconcile the CMB and LSS data with a broad spectrum of Hubble constant values, encompassing those inferred from local measurements.
• Importantly, this study demonstrates that the constraints on the variation of fundamental constants imposed by the specific recombination history are not as stringent as previously assumed.