a120

About Hubble's law they use a gas system which expands
according to this law: a bubble emitted by an aqualung. When it reaches the surface,
the pressure becomes smaller and this bubble expands. Its size is proportional
to the inverse of the pressure. If some observer was sitting on a molecule and
observed the other, they should own, with respect to this observer, an escape
velocity proportional to distance. Underwater activities have something to do
with cosmology.

The universe is assimilated to an expanding gas. But random
"proper motion", corresponding to local turbulence, introduces a "noise" when
one wants to measure the radial velocity, corresponding to a given distance
d. For example, when Hubble measured the radial velocities of neighbouring
galaxies, like Andromeda, which moves towards us, he concluded that the universe
was shrinking. But it was just a local artifact, due to random velocities.

In the air you breathe molecules have a random (thermal
velocity) close to 400 m/s (notice it is close to the sonic velocity).

Similarly the random velocities of galaxies, in their
clusters, lie between 500 to 1000 km/s. So that if one wants to evaluate
correctly the escape velocity, he has to choose a sample of galaxies far enough
to have a radial escape velocity higher than this thermal velocity.

The measurement of radial velocity is very easy and accurate.
It is based on the red shift. But the difficulty is to evaluate the distances.
How far are these galaxies from us?

Historically, the galaxies were first called "nebulae".
Some people thought they were located inside our milky way. But Hubble himself
answered this question, finding a cepheid in Andromeda, which was pushed to
cosmological distance: more than two million light-years far from us.

At large distances it was very difficult to isolate a
cepheid in these gloomy spots. Then, the distance evaluation was a question
of opinion. During years the evaluation of the Hubble's constant was controversial.
Many tended to values which fit the 15-20 billion years of the oldest stars
of our galaxies (from globular clusters). In the US, the French astronomer de
Vaucouleurs argued and tended to have different values.

All eyes were fixed on the space telescope Hubble.
In 1993 this one, with its sharp single eye, discovered cepheids in very distant
galaxies, located at ten million light years. At such distance the random
velocities were basically masked by the general radial velocity.

• Great, said the astronomers. We will have an accurate
  measure of the Hubble's constant Ho!

But, rapidly, the adventure transformed into a tragedy.
From 1993 to 1994, Hubble's measurement of these galaxies, 48 and 55 light
years distant, were 40% found closer by (with respect to oldest distance
evaluations)! So that the age of the Universe became 40% shorter. In 1994
Nature talked of 8-9 billion years......

He was younger than its own stars. Immediately the astrophysicists
and cosmologists tried to save the old good Standard Model and turned immediately
towards the cosmological constants, like firemen, facing an intellectual
cosmic fire, searching nervously for an extinguisher.

This constant was rapidly pulled out of its mothballs
and reactivated. On the figure (108) you can see the impact of this constant
on the expansion.

(108)

Some astrophysicists said:

• These new measurements, performed by Hubble space telescope,
  are nothing but a method to scale the cosmological constant. Now, we know
  its value!....

Few years later, what about this problem.

Two new facts: The satellite Hipparcos had performed
accurate measurements on distant stars, based on parallax. Then astronomers
changed the cepheid calibration.

• The objects are farther than we thought before. We have
  recalibrated them.

Andromeda was pushed away, from 2.5 billion years to
3.5 billion years.

• Wouffff.....

The evaluation of the age of the oldest stars of our galaxy
was revised too. Everybody did his best.

By the way, the model "universe interacting with a ghost
universe" (see Geometrical physics A) gives another decoding of Ho's measurements,
giving an older universe.