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| Alexander Friedmann (Александр Фридман) |
This post completes a previous post with a similar title:
The problem of the cosmological constant.First of all, we should define three different
concepts that could be closely related:
- Vacuum energy: due to the constant appearance of pairs of
particles and antiparticles that immediately mutually disintegrate, so they
are undetectable through direct experimentation. Their appearance is a
consequence of the uncertainty principle: ΔE×Δt<ħ/2,
which implies that a particle with energy ΔE
can appear spontaneously during a time Δt<ħ/(2ΔE),
which is smaller for larger ΔE.
Thus, a virtual electron would last less than 4×10-21 seconds.
A proton, whose mass is 1837 times greater, would last 1837 times less. By
applying quantum field theory to all the known particles, the energy of
the vacuum can be estimated.
- The cosmological constant: introduced by Einstein in his cosmological equation, which in the format devised by Alexander Friedman is expressed as follows: The symbol Λ is the cosmological constant. Einstein proposed a negative value, to compensate for a cosmic expansion, in which he initially did not believe. Today it is thought to be positive, which would explain the accelerated expansion of the universe discovered in 1998.
What is the relationship between these three
concepts? Vacuum energy could be the cause of the appearance of the
cosmological constant in the Friedman equation, which in turn would cause the
accelerated expansion of the universe. The value of the cosmological constant, as
a function of the vacuum energy, would be Λve=(8πG/c4)×ρv, where
G is the gravitational constant, c the speed of light, and ρv the
energy density of the vacuum. If this were true, dark energy would be another
name for vacuum energy.
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| Albert Einstein |
What is the mystery of the cosmological constant?
If we calculate its value based on the vacuum energy, by applying quantum field
theory to all the known elementary particles and adding the results, we get a
value 120 orders of magnitude greater than the value we get if we identify the
cosmological constant with dark energy and get its value from the standard
cosmological model. In other words: Λve = Λde×10120.
It has been said that this is the worst
prediction in the history of physics.
How could this mystery be solved? Perhaps this
way: the cosmological constant may not be derived exclusively from the energy
of the vacuum; its total value, Λde, would
be obtained by adding three components:
•
A basic (or bare) cosmological constant, due to
gravity.
•
Λve, the value calculated from the vacuum energy.
•
Another set of terms obtained in the same way,
corresponding to all those particles that we have not yet discovered, which could
also make a contribution.
The problem is that the total value, Λde, is
120 orders of magnitude smaller than the second component. We should assume
that the other two terms must almost exactly
compensate for this huge value, so the sum of the three terms would be so
small. This is a case of fine tuning, as the value of the
cosmological constant must be so small for life to be possible in our universe.
If it were larger, the universe would have expanded so quickly that galaxies would
not have formed, and if it were smaller than a small negative value it would
have collapsed a long time ago in a Big Crunch.
Almost exactly, but
not exactly. If the cosmological constant were exactly equal to zero, it would
be compatible with life and we could surmise that unknown reasons make the
three components compensate. But since it is almost zero, but positive (as the
accelerated expansion of the universe seems to indicate), there is no reason
for it to adopt that value, unless the universe has been designed just so on
purpose. Yes, to avoid this conclusion, some people say that there are a huge number
of universes and that we must be in one that is compatible with our existence, i.e.
the anthropic principle applied to some theory of the multiverse.
But these are not scientific solutions, but speculations.
Has anyone tried to solve the mystery in any
other way? Of course! But in almost all attempts it was necessary to replace Einstein’s
equations (general relativity) by something else: either making a drastic
adjustment of these equations, which have worked so well till now, or by
assuming the existence of an unknown fifth fundamental interaction (the quintessence). An attempt is being made to
analyze gravitational waves, which have been detected in the last
decade, to see if they shed any light on the problem. In the words of Gregory Gabadadze,
a professor at New York University: Since
1960, every generation of physicists has seen new proposals emerge. Perhaps someday
we’ll make predictions that we can verify, but we are not at that point yet.
Thematic Thread about Standard Cosmology: Previous Next
Manuel Alfonseca
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