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

Understand

The current Hubble constant tension is usually presented by comparing constraints on $H_0$ only.

• However, the post-recombination background cosmic evolution is determined by two parameters in the standard $\Lambda$CDM model, the Hubble constant ($H_0$) and today's matter energy fraction ($\Omega_{\rm{m}}$).
• If we therefore compare all constraints individually in the $H_0$-$\Omega_{\rm{m}}$ 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 $H_0$-$\Omega_{\rm{m}}$ space based on a flat $\Lambda$CDM model, treating them as separately as possible.