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The "model" of dark matter
...As mentioned above, there is an impressive list of problems related to astrophysics alone. For example, galaxies rotate too quickly. The observed mass is only 3 to 5 times too small to counteract the centrifugal force. The situation is even worse for galaxy clusters. This is an old problem, first noted decades ago by Fritz Zwicky.
...How to resolve this? Should Newton's law be revised? Some have simply suggested that galaxies, galaxy clusters, and even the entire universe might contain within them a mass (contributing to the gravitational field) that has so far escaped observation. What could this be? For instance, extremely dim stars. These objects were given a name: MACHOs (Massive Compact Halo Objects—massive, compact objects located in the galactic halo, the region of space surrounding and extending beyond the galactic disk). Detection method: occultation of background sources, mainly stars. Technique: monitor a very large number of stars and detect temporary decreases in brightness, whose time evolution would differ from those of variable stars.
Results: disappointing.
...Another hypothesis: "exotic particles," for example, massive neutrinos (possessing a small mass). However, no evidence has yet been found for the possible mass of neutrinos.
...Another candidate, favored by astrophysicist Françoise Combes: cold hydrogen at extremely low temperatures, thus nearly undetectable.
...This dark matter would then account for the strong gravitational lensing effects apparently associated with galaxies and galaxy clusters (gravitational arcs). Many consider these effects "irrefutable proof" of the existence of this undetected matter.
...It then becomes possible to explain anything and everything by skillfully sprinkling dark matter throughout the universe, in the right places. Thus, it is a perfectly ad hoc theory. Some researchers don't even bother to justify the origin, nature, or dynamics of this component, contenting themselves with claiming it's a new astronomy—“where we now map the invisible.” Research teams are actively working to produce maps of the distribution of dark matter.
...This dark matter helps tie together the large-scale structure of the universe, thus “justifying” it. Elsewhere, the distribution of dark matter is constructed not only to explain the cohesion of galaxies but also the shape of their rotation curves. All this is published abundantly and without difficulty (Astrophysical Journal, Astronomy and Astrophysics, etc.). The distinction is made between “cold dark matter” and “hot dark matter.”
Thus, some speculations appear “legitimate.”
The question of the cosmological constant and the age of the universe.
Let us first examine its origin. Given his field equation:
**S = **c T
...Einstein immediately sought to construct a model of the universe (1917). But since he did not know the universe was non-stationary, he tried to build a stationary model. He soon encountered numerous problems and visited the French mathematician Elie Cartan, who told him:
- You can modify your equation. I propose:
**S = **c T - Lg ** **
where **g **is the metric tensor and **L a constant. That way, the equation remains properly tensorial and your solution remains invariant under coordinate transformations.
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But what is the physical meaning of this constant L?
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That, my dear fellow, is your problem. I am a mathematician...
From a field equation, assuming weak curvature and low thermal velocities compared to the speed of light c, one can recover Newtonian dynamics. Newton's force then acquires a corrective term:
...This corrective term is thus proportional to distance. The term "repulsive power of the vacuum" is commonly used (or attractive, depending on the chosen sign of this arbitrary constant L).
...This repulsive power of the vacuum was the cornerstone that allowed Einstein's stationary universe to achieve equilibrium (though unstable, in fact). But very soon:
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Edwin Hubble's discovery revealed a redshift z, interpreted as a general cosmic expansion (Doppler effect). Thus, goodbye to the stationary universe model.
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At the same time, Russian physicist Friedmann derived non-stationary solutions to the field equation, without a cosmological constant.
Displeased, Einstein retreated under his tent, saying:
- If I had known the universe was non-stationary, I would have found it before Friedmann!
...The cosmological constant then sank into near oblivion for decades. Some argued for its necessary nullity. The fact is that, referring to actions over very large distances, it only manifests its effect late, when the characteristic dimension R(t) of the universe reaches “a sufficient value.”
...Measurements of redshift and radial velocities of galaxies allow calibration of Hubble's law, derived from the field equation, which simply states:
The recession velocity is proportional to the redshift z
The constant of proportionality is called the Hubble constant Ho.
...A brief aside for those unaware: An atom, stationary in the lab relative to the measuring device, emits radiation corresponding to a wavelength λ. Due to the Doppler effect, the same atom in motion produces a wavelength: λ' = λ + Δλ
We define:
| Δλ |
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| Δλ |
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If Δλ is positive: the source is receding—redshift.
If Δλ is negative, the source is approaching—“blueshift.”
The Hubble constant also appears in the law of expansion R(t) as a function of time:
...In fact, there are three Friedmann models, differing only in their description of the distant future of the cosmos.
In the diagram below, where we are supposed to be “far enough” from the distant future of the universe, the three curves coincide.
...Thus, knowledge of the cosmological expansion law and the Hubble constant immediately allows, according to this model (with zero cosmological constant), the deduction of the universe's age.
...Imagine taking an instantaneous photograph of a grenade explosion. The exposure time would produce some blur on objects, allowing estimation of their speed, thus enabling calculation—by examining just one photo—of when the explosion began. Of course, the cosmic explosion differs from a grenade explosion in its dynamics, since gravity, by slowing expansion, gradually decelerates it.
...Cosmic objects exhibit proper motions, similar to the thermal agitation of gas molecules. Hence the term “cosmological fluid”—a “gas” whose molecules are galaxies.
...To estimate the Hubble constant, measurements had to be based on sufficiently distant objects, thus moving at sufficiently high speeds to exceed the average thermal velocity...