Hubble tension: a short review of theoretical explanations

Abstract

The $\Lambda$ cold dark matter model successfully describes a wide range of cosmological observations. However, the persistent discrepancy between the value of the Hubble constant inferred from cosmic microwave background (CMB) measurements within this model and that obtained from local distance-ladder determinations points to a significant inconsistency. This short review examines theoretical responses across the cosmological inference chain, from the gravitational field equations to the pre-recombination sound horizon and the late-time distance-redshift relation. It discusses early-time and late-time mechanisms, as well as modified gravity, as ways to alter the acoustic ruler, distances, structure growth, or gravitational response. Current proposals can reduce the nominal tension, but often at the cost of correlated shifts in CMB spectra, standard-ruler distances, lensing, structure growth, or calibrator information. Further progress requires unified likelihoods and multi-probe tests linking all key observables under the same model assumptions.

51 pages, 13 figures, a short review prepared by invitation for RAA special topics