Accordingly to this article: https://medium.com/the-cosmic-companion/is-the-universe-younger-than-we-thought-e8a649a32ec8
"Is the Universe Younger than We Thought?", is the age of the universe,
not 13,8 billion years, but 11 billion years old.
This seems, to me, a rather big shift, specific because it is based on gravitational lensing.

Nicolaas Vroom

[[Mod. note -- This article is based on this press release
"High value for Hubble constant from two gravitational lenses"
https://www.mpa-garching.mpg.de/743539/news20190913
which in turn describes this research paper
"A measurement of the Hubble constant from angular diameter distances
to two gravitational lenses"
https://science.sciencemag.org/content/365/6458/1134
which is nicely synopsized in this commentary
"An expanding controversy"
/An independently calibrated measurement fortifies the debate
around Hubble's constant/
https://science.sciencemag.org/content/365/6458/1076

Figure 6 of the /Science/ research article gives a nice comparison
of some of the recent Hubble-constant measurements, showing that the
choice of cosmological model (at least within the range of models
considered by the authors) makes rather little difference.
-- jt]]

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XPost: sci.astro

Details at
https://www.iau.org/news/pressreleases/detail/iau1910/?lang

This one looks like a comet, but observations are just beginning.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swillner@cfa.harvard.edu Cambridge, MA 02138 USA

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In article <71609d81-f915-4d7d-baa4-e950a08810a0@googlegroups.com>,
Nicolaas Vroom <nicolaas.vroom@pandora.be> writes:

Accordingly to this article: https://medium.com/the-cosmic-companion/is-the-universe-younger-than-we-t=

hought-e8a649a32ec8

"Is the Universe Younger than We Thought?", is the age of the universe,
not 13,8 billion years, but 11 billion years old.
This seems, to me, a rather big shift, specific because it is based on gravitational lensing.

All else being equal, the age of the universe is inversely proportional
to the Hubble constant.

The headline doesn't deserve any prizes. There are many measurements of
the Hubble constant, and the field has a history of discrepant
measurement (i.e. measurements which differ by significantly more than
their formal uncertainties). Recently, the debate has shifted from "50
or 100?" to "67 or 73?" but since the formal uncertainties have also
gone down, one could argue that the "tension" is comparable to that in
the old days. There is more than one measurement supporting 67, and
more than one supporting 73. So, ONE additional measurement doesn't
mean "the textbooks will have to be rewritten" or some such nonsense,
but rather is an additional piece of information which must be taken
into account.

It should be noted that there are many measurements of the Hubble
constant from gravitational lenses. Not all agree. The biggest source
of uncertainty is probably the fact that the result depends on knowing
the mass distribution of the lens galaxy.

For what it's worth, I am co-author on a paper doing this sort of thing:

http://www.astro.multivax.de:8000/helbig/research/publications/info/0218= .html

Our value back then, almost 20 years ago, was 69+13/-19 at 95%
confidence. The first two authors recently revised this after
re-analysing the data, arriving at 72+/-2.6 at 1 sigma, though this
includes a better (published in 2004) lens model as well. The papers
are arXiv:astro-ph/9811282 and arXiv:1802.10088. Both are published in
MNRAS (links to freely accessible versions are at the arXiv references
above). It's tricky to get right. As Shapley said, "No one trusts a
model except the man who wrote it; everyone trusts an observation except
the man who made it." :-)

The above uses just the gravitational-lens system to measure the Hubble constant. Such measurements have also been made before for the two lens systems mentioned in the press release. What one actually measures is basically the distance to the lens. Since the redshift is known, one
knows the distance for this particular redshift; knowing the redshift
and the distance gives the Hubble constant. In the new work, this was
then used to calibrate supernovae of with known redshifts. (Determining
the Hubble constant from the magnitude-redshift relation for supernovae
is also possible, of course (and higher-order effects allow one to
determine the cosmological constant and the density parameter
(independently of the Hubble constant), for which the 2011 Nobel Prize
was awarded), but one needs to know the absolute luminosity, which has
to be calibrated in some way. Since they measure the distance at two
separate redshifts, the cosmology cancels out (at least within the range
of otherwise reasonable models). Their value is 82+/-8, which is
consistent with the current "high" measurements. There are many reasons
to doubt that the universe is only 11 billion years old, so a value of
73 is probably about right.

The MPA press release is more carefully worded: "While the uncertainty
is still relatively large" and notes that the value that that inferred
from the CMB. However, many would say that the anomaly is that the CMB
(in particular the Planck data) seem to indicate a low value.

Figure 6 of the /Science/ research article gives a nice comparison
of some of the recent Hubble-constant measurements, showing that the
choice of cosmological model (at least within the range of models
considered by the authors) makes rather little difference.
-- jt]]

In principle, the cosmological model can make a difference, but these
days we believe that the values of lambda and Omega have been narrowed
down enough that there isn't much room to move; measuring the distance
at two different redshift essentially pins it down.

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In article <71609d81-f915-4d7d-baa4-e950a08810a0@googlegroups.com>,
Nicolaas Vroom <nicolaas.vroom@pandora.be> writes:

Accordingly to this article: https://medium.com/the-cosmic-companion/is-the-universe-younger-than-we-thought-e8a649a32ec8

which in turn describes this research paper
"A measurement of the Hubble constant from angular diameter distances
to two gravitational lenses"
https://science.sciencemag.org/content/365/6458/1134

The paper is behind a paywall, but the Abstract, which is public,
summarizes the results. Two gravitational lenses at z=0.295 and
0.6304 are used to calibrate SN distances. The derived Hubble-
Lemaitre parameter H_0 is 82+/-8, about 1 sigma larger than other
local determinations and 1.5 sigma larger than the Planck value.

As Phillip wrote, the observations have their uncertainties, but 50
or so lenses would measure H_0 independently of other methods.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swillner@cfa.harvard.edu Cambridge, MA 02138 USA

[[Mod. note -- I've now found the preprint -- it's arXiv:1906.06712.
Sorry for not including that in my original mod.note. -- jt]]

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Steve Willner <willner@cfa.harvard.edu> wrote:

which in turn describes this research paper
"A measurement of the Hubble constant from angular diameter distances
to two gravitational lenses"
https://science.sciencemag.org/content/365/6458/1134

The paper is behind a paywall, but the Abstract, which is public,
summarizes the results. [[...]]

In a moderator's note, I wrote

[[Mod. note -- I've now found the preprint -- it's arXiv:1906.06712.
Sorry for not including that in my original mod.note. -- jt]]

Oops, /dev/brain parity error. The preprint is 1909.06712
repeat 1909.06712. Sorry for the mixup. -- Jonathan

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In article <mt2.1.4-81115-1569549391@iron.bkis-orchard.net>,
"Jonathan Thornburg [remove -animal to reply]"
<jthorn@astro.indiana-zebra.edu> writes:

The preprint is 1909.06712

Two additional preprints are at
https://arxiv.org/abs/1907.04869 and
https://arxiv.org/abs/1910.06306
These report direct measurements of gravitational lens distances
rather than a recalibration of the standard distance ladder.

The lead author Shajib of 06306 spoke here today and showed an
updated version of Fig 12 of the 04869 preprint. The upshot is that
the discrepancy between the local and the CMB measurements of H_0 is
between 4 and 5.7 sigma, depending on how conservative one wants to
be about assumptions. The impression I got is that either there's a
systematic error somewhere or there's new physics. The local H_0 is
based on two independent methods -- distance ladder and lensing -- so
big systematic errors in local H_0 seem unlikely. The CMB H_0 is
based on Planck with WMAP having given an H_0 value more consistent
with the local one. "New physics" could be something as simple as
time-varying dark energy, but for now it's too soon to say much.

One other note from the talk: it takes an expert modeler about 8 months
to a year to model a single lens system. Shajib and others are trying
to automate the modeling, but until that's done, measuring a large
sample of lenses will be labor-intensive. Even then, it will be
cpu-intensive. Shahib mentioned 1 million cpu-hours for his model of
DES J0408-53545354, and about 40 lenses are needed to give the desired precision of local H_0.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swillner@cfa.harvard.edu Cambridge, MA 02138 USA

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In article <qo590f$c75$1@dont-email.me>, willner@cfa.harvard.edu (Steve Willner) writes:

Two additional preprints are at
https://arxiv.org/abs/1907.04869 and
https://arxiv.org/abs/1910.06306
These report direct measurements of gravitational lens distances
rather than a recalibration of the standard distance ladder.

The upshot is that
the discrepancy between the local and the CMB measurements of H_0 is
between 4 and 5.7 sigma, depending on how conservative one wants to
be about assumptions.

"New physics" could be something as simple as
time-varying dark energy

Now THAT'S an understatement! :-)

Also interesting on this topic: arXiv:1910.02978, which suggests that
the local Cepheid measurements are the odd ones. arXiv 1802.10088
re-analyses data on one lens system, resulting in a slightly longer time
delay and hence slightly lower Hubble constant, i.e. making this
particular system more consistent with the CMB value. Steve mentioned
how long the modelling takes. A modeller has the input data, though;
there is a huge amount of work just to get that far as well: observing, reducing the data, and so on.

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On 19/10/15 10:17 PM, Steve Willner wrote:

In article <mt2.1.4-81115-1569549391@iron.bkis-orchard.net>,
"Jonathan Thornburg [remove -animal to reply]"
<jthorn@astro.indiana-zebra.edu> writes:

The preprint is 1909.06712

Two additional preprints are at
https://arxiv.org/abs/1907.04869 and
https://arxiv.org/abs/1910.06306

...
...

One other note from the talk: it takes an expert modeler about 8 months
to a year to model a single lens system. Shajib and others are trying
to automate the modeling,

You obviously do not mean that they do it by pencil and paper at this
moment. So why is modeling labor-intensive? Isn't it just putting a
point mass in front of the observed object, which only requires fitting
the precise position and distance of the point mass using the observed
image? (And if so, is the actual imaging with the point mass in some
place the difficult part?) Or is the problem that the lensing object
may be more extended than a point mass? (Or is it something worse!?)

--
Jos

[[Mod. note -- In these cases the lensing object is a galaxy (definitely
not a point mass!). For precise results a nontrivial model of the
galaxy's mass distribution (here parameterized by the (anisotropic)
velocity dispersion of stars in the lensing galaxy's central region)
is needed, which is the tricky (& hence labor-intensive) part.
-- jt]]

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In article <5da63082$0$10257$e4fe514c@news.xs4all.nl>, Jos Bergervoet <jos.bergervoet@xs4all.nl> writes:

On 19/10/15 10:17 PM, Steve Willner wrote:

In article <mt2.1.4-81115-1569549391@iron.bkis-orchard.net>,
"Jonathan Thornburg [remove -animal to reply]"
<jthorn@astro.indiana-zebra.edu> writes:

The preprint is 1909.06712

Two additional preprints are at
https://arxiv.org/abs/1907.04869 and
https://arxiv.org/abs/1910.06306

...
...

One other note from the talk: it takes an expert modeler about 8 months
to a year to model a single lens system. Shajib and others are trying
to automate the modeling,

You obviously do not mean that they do it by pencil and paper at this
moment.

Right; it's done on computers these days. :-)

So why is modeling labor-intensive? Isn't it just putting a
point mass in front of the observed object, which only requires fitting
the precise position and distance of the point mass using the observed
image?

A point mass could be done with pencil and paper.

(And if so, is the actual imaging with the point mass in some
place the difficult part?) Or is the problem that the lensing object
may be more extended than a point mass? (Or is it something worse!?)

[[Mod. note -- In these cases the lensing object is a galaxy (definitely
not a point mass!). For precise results a nontrivial model of the
galaxy's mass distribution (here parameterized by the (anisotropic)
velocity dispersion of stars in the lensing galaxy's central region)
is needed, which is the tricky (& hence labor-intensive) part.
-- jt]]

Right.

In addition to the time delay, which depends on the potential, one fits
the image positions, which depend on the derivative of the potential,
and can also choose to fit the brightness of the images, which depends
on the second derivative of the potential. (Since the brightness can be affected by microlensing, one might choose not to fit for it, or to
include a model of microlensing as well.) If the source is resolved,
then the brightness distribution of the source also plays a role.

Also, one can (and, these days, probably must) relax the assumption that
there is only the lens which affects the light paths. While in most
cases a single-plane lens is a good enough approximation, the assumption
that the background metric is FLRW might not be. In particular, if the
path is underdense (apart from the part in the lens plane, which of
course is very overdense), then the distance as a function of redshift
is not that which is given by the standard Friedmann model. At this
level of precision, it's probably not enough to simply parameterize
this, but rather one needs some model of the mass distribution near the
beams.

The devil is in the details.

Think of the Hubble constant as determined by the traditional methods (magnitude--redshift relation). In theory, one needs ONE object whose
redshift (this is actually quite easy) and distance are known in order
to compute it. In practice, of course, there is much more involved
(mostly details of the calibration of the distance ladder), though this
is still relatively straightforward compared to a detailed lens model.

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In article <qo67pc$csc$1@gioia.aioe.org>,
"Phillip Helbig (undress to reply)" <helbig@asclothestro.multivax.de> writes:

At this level of precision, it's probably not enough to simply
parameterize this, but rather one needs some model of the mass
distribution near the beams.

That's exactly right (at least to the extent I understood Shajib's
talk). In particular, one has to take into account the statistical distribution of mass all along and near the light path and also (as
others wrote) the mass distribution of the lensing galaxy
itself. It's even worse than that in systems that have multiple
galaxies contributing to the lensing. Not only do their individual
mass distributions matter, their relative distances along the line of
sight are uncertain and must be modeled.

Presumably all that can be automated -- at the cost of many extra cpu
cycles -- but it hasn't been done yet.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swillner@cfa.harvard.edu Cambridge, MA 02138 USA

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In article <qodakb$mhe$1@dont-email.me>, willner@cfa.harvard.edu (Steve Willner) writes:

In article <qo67pc$csc$1@gioia.aioe.org>,
"Phillip Helbig (undress to reply)" <helbig@asclothestro.multivax.de> writes:

At this level of precision, it's probably not enough to simply
parameterize this, but rather one needs some model of the mass
distribution near the beams.

That's exactly right (at least to the extent I understood Shajib's
talk). In particular, one has to take into account the statistical distribution of mass all along and near the light path and also (as
others wrote) the mass distribution of the lensing galaxy
itself.

These effects, i.e. that the mass in the universe is at least partially distributed clumpily (apart from the gravitational lens itself, which
is, essentially by definition, a big clump), also influence the
luminosity distance, which of course can be used to determine not just
the Hubble constant but also the other cosmological parameters.
However, it's not as big a worry, for several reasons:

As far as the Hubble constant goes, the distances are, cosmologically
speaking, relatively small, whereas the effects of such small-scale inhomogeneities increase with redshift.

Whether at low redshift for the Hubble constant or at high redshift for
the other parameters, usually several objects, over a range of
redshifts, are used. This has two advantages. One is that these
density fluctuations might (for similar redshifts) average out in some
sense. The other is that the degeneracy is broken because several
redshifts are involved. (If the inhomogeneity is an additional
parameter which can also affect the distance as calculated from
redshift, with just one object at one redshift one can't tell what
effect it has, but since the dependence on redshift is different for the inhomogeneities, the Hubble constant, and the other parameters, then
some of the degeneracy is broken.)

At the level of precision required today, simply describing the effect
of small-scale inhomogeneities with one parameter is not good enough.
It does allow one to get an idea of the possible size of the effect,
though. To improve, there are two approaches. One is to try to measure
the mass along the line of sight, e.g. by weak lensing. Another is to
have some model of structure formation and calculate what it must be, at
least in a statistical sense.

There is a huge literature on this topic, though it is usually not
mentioned in more-popular presentations.

I even wrote a couple of papers myself on this topic:

http://www.astro.multivax.de:8000/helbig/research/publications/info/etas= nia.html

http://www.astro.multivax.de:8000/helbig/research/publications/info/etas= nia2.html

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In article <qo590f$c75$1@dont-email.me>, I wrote:

The upshot is that the discrepancy between the local and the CMB measurements of H_0 is between 4 and 5.7 sigma, depending on how
conservative one wants to be about assumptions.

We had another colloquium on the subject yesterday. Video at https://www.youtube.com/watch?v=K1496gv8KCo

The points I took away are: 1. both the local ("direct") measurements
and the distant ("indirect") measurements are made by two
_independent_ methods, which agree in each case. That is, the two
direct methods (SNe, lensing) agree with each other, and the two
indirect methods (CMB, something complicated) agree with each other,
but the direct and indirect measurements disagree.

2. contrary to what I wrote earlier, even a non-physical change of
dark energy with time (say an abrupt increase at some fine-tuned
epoch) cannot fix the disagreement.

3. while there have been several suggestion for new physics to fix
the problem, none of them so far seems to work without disagreeing
with other data.

What fun!

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swillner@cfa.harvard.edu Cambridge, MA 02138 USA

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On 19/11/02 9:50 AM, Steve Willner wrote:

...

...> 1. both the local ("direct") measurements

and the distant ("indirect") measurements are made by two
_independent_ methods, which agree in each case. That is, the two
direct methods (SNe, lensing) agree with each other, and the two
indirect methods (CMB, something complicated) agree with each other,
but the direct and indirect measurements disagree.

2. contrary to what I wrote earlier, even a non-physical change of
dark energy with time (say an abrupt increase at some fine-tuned
epoch) cannot fix the disagreement.

Indeed someone asks this question at http://youtu.be/K1496gv8KCo?t=3785
(at about z=10^(10) in the video, I believe..) and the answer given is
that it cannot be an abrupt change, "it must be smooth". The presenter's
answer seems to invoke (partly) other observations that rule it out. (So
change in dark energy might fix it but create new disagreements, which
would bring it in category 3, below.. Or would the discrepancy already
be in matching the data actually discussed here?)

3. while there have been several suggestion for new physics to fix
the problem, none of them so far seems to work without disagreeing
with other data.

What fun!

Yes! So why are only 20 people attending?!

--
Jos

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On 02 Nov 2019, willner@cfa.harvard.edu (Steve Willner) wrote:

3. while there have been several suggestion for new physics to fix
the problem, none of them so far seems to work without disagreeing
with other data. ... What fun!

How about a migrating space-time curvature? Can that connect the two
places? It would have the effect of making distant places dimmer.
Try it in a static universe also, its effects simulate FRW.

[[Mod. note -- I think this is on the edge of our newsgroup ban on
"excessively speculative" submissions, but clearly *something* odd
is going on.

I wonder if it could be "just" non-uniformity in the Hubble flow
in the region of the "local" measurements?
-- jt]]

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In article <5dbd814d$0$10260$e4fe514c@news.xs4all.nl>,
Jos Bergervoet <jos.bergervoet@xs4all.nl> writes:

Yes! So why are only 20 people attending?!

Attendance was far higher than that. The video shows only one side
of the main floor of the room, and the other side is far more popular
(perhaps because it has a better view of the screen). There's a
balcony as well, and quite a few people leave at the end of the talk
and before the question period. I didn't count, but I think the
attendance was close to 100. Anyway it was about the normal number
for a colloquium here.

The colloquium list for the fall is at
https://www.cfa.harvard.edu/colloquia
if you want to see what other topics have been covered.

To the question in another message, I don't see why some local
perturbation -- presumably abnormally low matter density around our
location -- wouldn't solve the problem in principle, but if this were
a viable explanation, I expect the speaker would have mentioned it.
It's not as though no one has thought about the problem. The
difficulty is probably the magnitude of the effect. I don't work in
this area, though, so my opinion is not worth much.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swillner@cfa.harvard.edu Cambridge, MA 02138 USA

[[Mod. note -- I apologise for the delay in posting this article,
which was submitted on Fri, 8 Nov 2019 21:15:25 +0000.
-- jt]]

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In article <qq4ltd$31f$1@dont-email.me>, Steve Willner <willner@cfa.harvard.edu> writes:

To the question in another message, I don't see why some local
perturbation -- presumably abnormally low matter density around our
location -- wouldn't solve the problem in principle, but if this were
a viable explanation, I expect the speaker would have mentioned it.
It's not as though no one has thought about the problem. The
difficulty is probably the magnitude of the effect. I don't work in
this area, though, so my opinion is not worth much.

I'm sure that someone must have looked at it, but is the measured Hubble constant the same in all directions on the sky? (I remember Sandage
saying that even Hubble had found that it was, but I mean today, with
much better data, where small effects are noticeable.) If it is, then
such a density variation could be an explanation (assuming that it would otherwise work) only if we "just happened" to be sitting at the centre
of such a local bubble.

Of course, some of us remember when the debate was not between 67 and
72, but between 50 and 100, with occasional suggestions of 42 (really)
or even 30. And both the "high camp" and "low camp" claimed
uncertainties of about 10 per cent. That wasn't a debate over whether
one used "local" or "large-scale" methods to measure it, but rather the deference depended on who was doing the measuring. Nevertheless, it is conceivable that there is some unknown systematic uncertainty* in one of
the measurements.

---
* For some, "unknown systematic uncertainty" is a tautology. Others,
however, include systematic uncertainties as part of the uncertainty
budget. (Some people use "error" instead of "uncertainty". The latter
is, I think, more correct, though in this case perhaps some unknown
ERROR is the culprit.

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On 11/2/19 3:50:25 AM, Steve Willner wrote:

In article <qo590f$c75$1@dont-email.me>, I wrote:

The upshot is that the discrepancy between the local and the CMB
measurements of H_0 is between 4 and 5.7 sigma, depending on how
conservative one wants to be about assumptions.

3. while there have been several suggestion for new physics to fix
the problem, none of them so far seems to work without disagreeing
with other data.

What fun!

In the question and answer period
One person asked if the triple point of hydrogen may provide
insight to the problem of discrepancy between the local
and the CMB measurements of H_0.
The triple point of hydrogen is at 13.81 K 7.042 kPa.
Silvia Galli didn't provide an answer
other than many things are possible.

The questioning person's name was not given.
Can anyone provide some insight
into what the triple point of hydrogen
has anything to do with discrepancy between
the local and the CMB measurements of H_0?

Richard Saam

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On 11/2/19 3:50:25 AM, Steve Willner wrote:
In article <qo590f$c75$1@dont-email.me>, I wrote:

The upshot is that the discrepancy between the local and the CMB
measurements of H_0 is between 4 and 5.7 sigma, depending on how
conservative one wants to be about assumptions.

3. while there have been several suggestion for new physics to fix
the problem, none of them so far seems to work without disagreeing
with other data.

What fun!

The Ho data is tightening:

**
Testing Low-Redshift Cosmic Acceleration with Large-Scale Structure https://arxiv.org/abs/2001.11044
Seshadri Nadathur, Will J. Percival,
Florian Beutler, and Hans A. Winther
Phys. Rev. Lett. 124, 221301 - Published 2 June 2020
we measure the Hubble constant to be
Ho = 72.3 +/- 1.9 km/sec Mpc from BAO + voids
at z<2

and

Ho = 69.0 +/- 1.2 km/sec Mpc from BAO
when adding Lyman alpha at BAO at z=2.34
**

Richard D Saam

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In article <9rednSTb2_1FxEfDnZ2dnUU7-K_NnZ2d@giganews.com>, "Richard D.
Saam" <rdsaam@att.net> writes:

The Ho data is tightening:

**
Testing Low-Redshift Cosmic Acceleration with Large-Scale Structure https://arxiv.org/abs/2001.11044
Seshadri Nadathur, Will J. Percival,
Florian Beutler, and Hans A. Winther
Phys. Rev. Lett. 124, 221301 - Published 2 June 2020
we measure the Hubble constant to be
Ho = 72.3 +/- 1.9 km/sec Mpc from BAO + voids
at z<2

and

Ho = 69.0 +/- 1.2 km/sec Mpc from BAO
when adding Lyman alpha at BAO at z=2.34
**

I guess it depends on what you mean by "tightening". If one
measurement is X with uncertainty A, and another Z with uncertainty
C, and they are 5 sigma apart, then someone measures, say, Y with
uncertainty B, which is between the other two and compatible with
both within 3 sigma, that doesn't mean that Y is correct. Of course,
if someone does measure that, they will probably publish it, while
someone measuring something, say, 5 sigma below the lowest measurement,
or above the highest, might be less likely to do so.

It could be that Y is close to the true value, but perhaps all are
wrong, or X is closer, or Z. The problem can be resolved only if
one understands why the measurements differ by more than a reasonable
amount.

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