Caption: The Hubble tension (direct value ≅ 73 (km/s)/Mpc; Λ-CDM fit value ≅ 67.5 (km/s)/Mpc) illustrated by the leftmost and rightmost data points.

Note the Hubble constant H_0 is the relative rate of the expansion of the universe. It is given in units of (km/s)/Mpc. So a Hubble constant of H_0 = 73 (km/s)/Mpc means that every megaparsec (Mpc) further out you go, the recession velocity relative to you of astronomical objects participating in the expansion of the universe increases by 73 (km/s).

Features:

1. Circa 2018, it was found that the Hubble constant by direct observations for the local observable universe was H_0 ≅ 73 (km/s)/Mpc and by global indirect measurements from the Planck spacecraft (2009--2013) was H_0 ≅ 67 (km/s)/Mpc.

   These determinations now disagree by more than 2 standard deviations (i.e., σ's): typically 4σ is cited circa 2025.

   So there is a tension that is approaching a falsification of the (BASE) Λ-CDM model and perhaps of the cosmological constant Λ (which is the simplest form of dark energy). This tension is the Hubble tension.

2. There are various extensions to the Λ-CDM model collectively called extended-Λ-CDM models.

   One or many or none of these may be adequate to account for the Hubble tension. But being adequate is NOT enough to confirm a theory to high confidence.

   The Λ-CDM model had an elegant simplicity that the extended-Λ-CDM models lack when viewed by Occam's razor. The extended-Λ-CDM models all seem ad hoc: just fix-ups.

   An extended-Λ-CDM model that can account for the Hubble tension and is motivated by an elegant theoretical reason is strongly desired.

3. One possible extension is to allow dark energy (whatever it actually is) to vary with cosmic time while still being constant in space.

   But we would like to have elegant theory of that variation.

4. Right now we need more guidance from observation and/or some elegant new theory to make progress in solving Hubble tension.

   Among other projects, the Roman Space Telescope (RST, c.2025--c.2030) and the Euclid (c.2021--c.2027) will supply cosmological statistics which should give us a much better idea of how dark energy behaves as a function of cosmic time.

5. The solution cosmological model to the Hubble tension might require a new name if it is too different from the Λ-CDM model.

   Perhaps, we will just call it the standard model of cosmology (SMC) which name is currently used sometimes for the Λ-CDM model itself.

   Actually, using SMC is a good idea since it allows us to update our standard model of cosmology without having to update the name.

6. Advances in cosmology are very exciting---but updating Introductory Astronomy Lectures (IAL) is a nuisance.