In article , Steve Willner
writes:=20

In article ,
"Richard D. Saam" writes:
The main point of the Space Telescope Institute work
https://arxiv.org/abs/1903.07603
is that 4.4 sigma discrepancy between Planck Ho and STI Ho is not=20
readily attributable to an error in any one source or measurement,=20
increasing the odds that it results from a cosmological feature beyond=
=20
LambdaCDM'.
=20
Indeed. Whatever it is, it doesn't seem to be statistics.

For historical reasons (remember the famous factor of 2?), people could=20
be forgiven for thinking that H_0 discrepancies would clear up---at=20
least for a while. This seems a real low-z vs. high-z issue, not an=20
issue with who is observing how and so on. It also doesn't seem to be=20
driven by prejudices. (I had the pleasure of hearing Allan Sandage=20
lecture at a Saas-Fee school back in 1993. The published version, in=20
The Deep Universe (together with contributions by the other two=20
lecturers, Malcolm Longair and Rich Kron), is an excellent introduction=20
to observational cosmology. In person, it was extremely clear that he=20
took the Einstein-de Sitter universe as given, due to inflation, which=20
of course means that H_0 has to be low to avoid the age problem. With=20
regard to observations, he was careful and critical (if sometimes=20
wrong), but here he drunk the inflation kool-aid hook, line, and sinker=20
(if I can be allowed to mix metaphors).

There is a workshop in Chicago in October on H_0 discrepancies.

The preprint (linked above) gives references to other work on the CMB
and BAO, which methods give the Hubble-Lemaitre parameter at high
redshift, i.e., early in the history of the Universe. A simple
summary is that dark energy appears to have increased over
cosmological time. =20

If dark energy can vary, then many things are possible, especially since=20
we have no idea why it should vary in a particular way (common=20
parameterizations are not based on any sort of theory).

Fig 4 of the preprint gives some ideas of why
that might have happened. Another possibility, of course, is that
there is some unrecognized systematic error in one of the
measurements. The local H_0 looks pretty solid to me. I know less
about the early H but can't help wondering about the calculated
sound-wave distances, which depend on baryonic physics.

I recently ran across this:

@ARTICLE { PFleuryDU13a ,
AUTHOR =3D "Pierre Fleury and H\'el\`ene Dupuy and"
Jean-Philippe Uzan,
TITLE =3D "Can All Cosmological Observations Be
Accurately Interpreted with a Unique
Geometry",
JOURNAL =3D PRL,
YEAR =3D "2013",
VOLUME =3D "111",
NUMBER =3D "9",
PAGES =3D "091302",
MONTH =3D aug
}

Here is my summary based on a quick glance:

They suggest that the well known `tension' between Planck and the m--z
relation for type Ia supernovae can be relieved if the calculations are
done with a Swiss-cheese model. This is because the CMB data have a
typical angular scale of 5 arcmin while the typical angular size of a
supernova is $10^{-7}$ arcsec. If the Swiss-cheese model is more
appropriate, but a homogeneous model assumed, then one will
underestimate H_0 and overestimate Omega_0.=20

Keep in mind that H_0 and Omega_0 are correlated in the CMB data.

The Swiss-cheese model takes a Friedmann-Lemaitre-Robertson-Walker
(FLRW) universe and removes some matter at certain places (creating the
holes), which is then placed in the center of the resulting hollow
spheres, either as a point mass, a spherical mass smaller than the hole,
or even something like an FLRW model inside the hole. This is not a=20
particularly accurate model for the universe, but it does have the=20
advantage of being an exact solution to the Einstein equations, so one=20
does not have to worry about the validity of approximations used in=20
other approaches (such as that used by Zeldovich, which is often known=20
as the Dyer-Roeder or ZKDR distance (the K being Kantowskii, who was=20
also one of the pioneers of this subject, and the D perhaps representing=20
Dashevskii instead, who was on two of the three early Soviet papers on=20
this topic (Zeldovich, Dashevskii & Zeldovich, Dashevskii and Slysh))).

There is a huge literature on such inhomogeneous models (and also on=20
more exotic inhomogeneous models), but I haven't notice that they have=20
been paid much attention in this context.