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How old is the universe ?
There are several methods to evaluate the age of the universe.
The first is to refer to the Bible. Then you get something like 5600 years.
But radioactive decay enforce people to enlarge this value.
The second method, based on dynamics of globular clusters,
is that they contain primeval stars, the oldest of our galaxy. This
method will be described later.
Third one : based on some cosmological model. Then one
starts from a field equation. Einstein had his own (but, as evoked in a preceding
section, Hilberth possibliy invented it....).
(101)
S = c T
From this equation ( 1915) Einstein immediatly tried to build
a model of the universe, where curvature could be identified to energy-matter
content. As he ignored that the universe was non-steady, he tried to build a
steady-state model. But he gots many problems. Then he visited the great French
mathematician Elie Cartan, who declared :
- My dear friend, Ican suggest you modify your field equation. What about
:
(102)
S = c T -Lg
where g is your metric tensor and L
some constant. Notice your equation has still tensor form, is coordinate-invariant
end divergenceless. Nice, isn't it ?
-
Yes, thanks a lot. But what could be the physical meaning
of this new "cosmological" constant L
? -
My good friend, it's your problem, not mine. I've done
my job. You know, I'm a mathematician, not a physicist...
Einstein was puzzled and worried. He thought that Newtonian
approximation could clear up the problem and bring some light on the ontologic
signification of this mysterious constant.
Newtonian approximation :
-
Small space curvature, weak field.
-
Velocities small with respect to light velocity c.
-
Quasi steady-state conditions ( with respect to the
general cosmic process : the universe, as a whole, is considered as if it
was "frozen" ).
Then the Newton's law get a corrective term :
(103)
Notice this corrective term is proportional to distance
r.It's a long range force. It can be attractive or repulsive? Depending on
the arbitrary sign of L
you choose. Considering this force was repulsive, it was possible to build
a steady-state universe, which Einstein did immediatly, where the mysterious
repulsive action of void balanced the normal attractive Newtonian force.
But this model was fairly unstable. If its space extension
was increased, the Newton force became weaker and the repulsion of void stronger,
and vice-versa. Einstein was more worried than ever.
Then two new facts occurred, almost at same time.
-
Edwin Hubble discovered the expansion of the universe.
-
The Russian glider' pilot Friedmann built a non-steady
solution of the (101) field equation ( no cosmological constant required ).
Einstein got mad about it and declared :
- If Iwas aware of universe's non-steady features,
Ishould have found before Friedmann !
If, as Lacedemonian used to say.....
Then the cosmologic constant passed into disuse, after
some time. Some astrophysicists built arguments in order to show that it should
necessarily be zero.
As this constant goes with a repulsive force which acts
only at very large distances, it modifies the evolution of the universe only
in late period, in a second era of expansion.
The Hubble's law simply says
(104)
The galaxies' running
away velocity is proportional to their red shift z
The constant of proportionality is called the Hubble's
constant Ho.
What about z ?
A steady atom, in lab, can emit radiation, if hot enough
( is a Busen flame ). This radiation corresponds to a nominal wavelength l.
If the atom is moving, with respect to the observer, this
last measure a different wavelength, due to Doppler's effect :
l' = l
- Dl
Or simply write :
(105)
If Dl >
0 : the source moves away : red shift.
Si Dl <
0 , the source gets closer : "blue shift".
There are three Friemann's models, as shown on figure
(106), which differ from their description of distant future. For hyperbolic
and parabolic model, the expansion never stops. For elliptic model, it finally
stops and the universe shrinks ( Big Crunch ).
(106)
Fgure (107) corresponds to the time "from now to the beginning",
where the three curves are almost identical. Then the model sets a simple
relation between the age of the universe and the Hubble's constant, shown
on the figure.
(107)
Imagine you take a picture of a grenade, just after explosion.
On your picture you can measure the velocities of the fragments, due to the
exposure time of your camera :
Notice that this velocity field does not correspond tu
Hubble's law.The fragments are projected with similar velocities :
From the picture one can calculate the interval of time
between the begenning of the grenade's explosion and the time when the picture
was taken. Then we can calculate the "age of the explosion".
Same thing for the Universe, except the expansion law
(107) is different : the expansion velocity was higher in the past.
Universe is assimilated to a gas, whose molecule would
be the galaxies. An expanding gas, with expansion velocity field, plus thermal
(random) velocities.
