Sommaire:

While the standard $\Lambda$CDM model provides an astonishing fit to cosmological data, there is a 4-6 $\sigma$ tension in the Hubble constant, $H_0$, between the value inferred from early-Universe observables, Planck CMB anisotropy spectra, and the value determined by local measurements from SH0ES collaboration using Type 1a SN calibrated with Cepheid variables. As an effort to solve this tension, we develop a method of searching for data-driven solutions to the Hubble tension given cosmological dataset, based on the standard Fisher bias formalism. As an example, we apply our method to time-varying electron mass modifying cosmological recombination history. With Planck CMB data, we find a solution entirely resolving the Hubble tension. However, once BOSS BAO and PantheonPlus uncalibrated SN data are included, it is not possible to fully solve the tension. The method we develop in this work can be a useful tool to search for any other possible extensions to the $\Lambda$CDM model, and is expected to inspire a model-building effort from the cosmology and particle physics community.

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