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A family of simple and minimal extensions of the standard cosmological$\Lambda$CDM model in which dark matter experiences an additional long-rangescalar interaction is demonstrated to alleviate the long lasting Hubble-tensionwhile letting primordial nucleosynthesis predictions unaffected and passing byconstruction all current local tests of general relativity. This articledescribes their theoretical formulation and their implications for dark matter.Then, it investigates their cosmological signatures, both at the background andperturbation levels. A detailed comparison to astrophysical data is performedto discuss their ability to fit existing data. A thorough discussion of thecomplementarity of the low- and high-redshift data and on their constrainingpower highlights how these models improve the predictions of the $\Lambda$CDMmodel whatever the combination of datasets used and why they can potentiallyresolve the Hubble tension. Being fully predictive in any environment, theypave the way to a better understanding of gravity in the dark matter sector.

The Hubble tension as a window on the gravitation of the dark matter sector: exploration of a family of models