Investigating the Hubble Constant Tension: Two Numbers in the Standard Cosmological Model

The current Hubble constant tension is usually presented by comparing constraints on H0 only. However, the postrecombination background cosmic evolution is determined by two parameters in the standard ΛCDM model, the Hubble constant (H0) and today's matter energy fraction (Ωm). If we therefore compare all constraints individually in the H0–Ωm plane, (1) various constraints can be treated as independently as possible, (2) single-sided constraints are easier to consider, (3) compatibility among different constraints can be viewed in a more robust way, (4) the model dependence of each constraint is clear, and (5) whether or not a nonstandard model is able to reconcile all constraints in tension can be seen more effectively. We perform a systematic comparison of different constraints in the H0–Ωm space based on a flat ΛCDM model, treating them as separately as possible. Constraints along different degeneracy directions consistently overlap in one region of the space, with the local measurement from Cepheid variable–calibrated supernovae being the most outlying, followed by the time-delay strong-lensing result. Considering the possibility that some nonstandard physics may reconcile the constraints, we provide a general discussion of nonstandard models with modifications at high, mid, or low redshifts and the effect of local environmental factors. Due to the different responses of individual constraints to a modified model, it is not easy for nonstandard models to reconcile all constraints if none of them have unaccounted-for systematic effects.