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Regarding Hubble's law, a gaseous system that expands according to this law is used: a bubble emitted by a scuba tank. When it reaches the surface, the pressure decreases and this bubble expands. Its size is proportional to the inverse of the pressure. If an observer were sitting on a molecule and observing the others, he should notice, with respect to himself, an escape velocity proportional to the distance. Subaquatic activities have something to do with cosmology.
The universe is assimilated to an expanding gas. But random "proper motions", corresponding to local turbulence, introduce 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 neighboring 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 speed of sound).
Similarly, the random velocities of galaxies, within their clusters, lie between 500 to 1000 km/s. So, if one wants to evaluate correctly the escape velocity, one 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, 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 at a cosmological distance: more than two million light-years away from us.
At large distances, it was very difficult to isolate a Cepheid in these dark regions. Then, the distance evaluation was a question of opinion. For years, the evaluation of the Hubble 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 the 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 a 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 constant H₀!
But, rapidly, the adventure transformed into a tragedy. From 1993 to 1994, Hubble's measurements of these galaxies, 48 and 55 million light years distant, were found 40% closer (with respect to the oldest distance evaluations)! So that the age of the Universe became 40% shorter. In 1994, Nature talked of 8-9 billion years......
It 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 constant, 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, is nothing but a method to scale the cosmological constant. Now, we know its value!...
A 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 recalibrated the Cepheids.
- The objects are farther than we thought before. We have recalibrated that.
Andromeda was pushed away, from 2.5 billion years to 3.5 billion years.
- Whew!
The evaluation of the age of the oldest stars of our galaxy was revised too. Everybody did their best.
By the way, the model "universe interacting with a ghost universe" (see Geometrical Physics A) offers another interpretation of Ho's measurements, leading to an older universe.