A few words on DE, Branes, Expansion of the Universe, and "stuff".
Version : 0.7.
Date : 24/06/2010
By : Albert van der Sel
Type of doc : This is my note. It's Just a few speculations. But... hopefully you like them.
You might know, that the latest insights tells us, that the Universe is expanding at an increasing rate.
What's really weird is, that (since the Big Bang) the Universe expanded, but gradually slowed down in the rate, due to gravity.
Then, for whatever reason, the acceleration seemed picked up momentum again. And that's the weird part.
Note: the effect is likely to be real, but is still questioned by a number of scientists.
As it looks now, the Universe will expand faster and faster, until there's nothing left anymore,
as if the vacuum will fully decay "into something" we don't exactly know about.
There are idea's allright in the scientific community. Like for example "Dark Energy" (DE) which is supposed to exert
a "negative" pressure, which counteracts gravity.
DE is believed to be about 70% of the total energy of the present Universe. This then, causes the expansion
of the Universe to accelerate.
Now, to what DE actually is, some argue, that it is just the "vacuum energy density". They say that wo do not need
to look further for some other exotic field.
Still, some others say that the "vacuum energy density" is (globally) "constant" and see that as problematic for the acceleration.
They then postulate an additional sort of space-time varying field, that recently went 'stronger' and now drives the acceleration.
Still another, but probably wrong, easy viewpoint could be this:
Dark Energy could possibly be some unknown field, that always has exerted a certain pressure.
Now, since the matter (sort of) dilutes with the expansion, we can imagin that at some point, the Dark Energy
starts to "outwin" gravity, resulting in faster and faster expansion.
It's just like some "imbalance" starts to occur at some point: as the total of matter expands, that is, sort of dillutes,
the gravitation gradually gets "weaker" and weaker.
Then, the negative pressure gets relatively stronger and stronger, compared to the gravity, and thus acceleration is unavoidable.
But as said before, this is not accepted much by scientists, and most of them "bet their horses" on some strange field
that long ago was weak, and got stronger, which effect is somehow related to space and time.
Also, but not often heard, are viewpoints that relate a 3 brane with closed strings, as regular particles with
a number of know forces (like electromagnetic, nuclear, weak force) on the one side, and closed strings
like gravitons, on the other side, wich are able to leak away into the higher dimensional superspace.
This then, could contribute to the effects we observe in our Universe (our brane).
There are many viewpoints that "more or less" relate to the above.
Below are just a few considerations, (but be warned: they could be totally wrong...!)
Remark: it's perhaps best to read the note "1.1 Short simplified Overview on DE and the acceleration of the Universe", first.
Note 1: gravitons escaping our D brane.
Superstring theory predicts the existence of new objects, called p-branes (where p is the number of spatial dimensions they occupy)
Certain p-branes are called D-branes. They have the property that strings can end on them.
It's tempting to view the observable Universe as a 3-brane, which is embedded in a space with 6 additional spatial dimensions (the bulk)
.
So, our "standard particles" (photons, quarks and leptons), exist only in three-dimensional subspace: the three-brane.
But there are also those hidden (extra) dimensions, which is known, as said before, as "the bulk".
Note: The idea that the universe (that is particles) is trapped on a membrane ("brane") in some high-dimensional space-time,
might even explain why gravity is so weak, compared to other forces.
Actually, the theory permits sets of three-branes, resulting in multiple independent Universes.
Each universe takes the form of a D-brane. Objects in each universe are essentially
confined to the D-brane of their universe, but may (or may not) be able to interact with other universes.
For example, gravity, or gravitons, which are closed strings, not with their endfoots placed on D-branes,
may be able to leak away from their Universe.
In the figure on the left, you see the regular particles which are bound on their three-brane,
while the gravitons (which are closed strings) are not, and are probably able to vanish from the Universe.
Some theorist even goes that far as saying that gravity actually is, (or wants to), "living in the bulk", meaning that
it's more natural for gravitons to leak from our 3-brane to the bulk.
It's not impossible that large accelerator experiments, will show that a collision (e.g. of a proton and anti-proton),
will produce (among other familiar particles), a graviton, which might escapes to the bulk.
We, on the 3 brane, might then observe an imbalance in energy, which supports the upper theory.
So, if this scenario is really true, why does one need Dark Energy to explain the acceleration of the Universe?
Since gravitons "like to flee away" to the bulk anyway, then overall gravity in/on our Brane lowers, so.. there you are!
Well, that exlanation is, to some degree, doubtfull and really to easy.
Some folks argue in the following way:
Forces like electromagnetism and the nuclear force, only operate in our 3 spatial dimensions, that is, in the 3-brane,
while gravity operates in all spatial 10 dimensions, so out of the 3 brane as well.
For now, I think we can conclude that "escaping gravitons" is likely no alternative for Dark Energy.
Or is it? Anyway, most scientists don't believe that.
So, in the next sections, more "accepted" models will be discused.
Note: the following is very speculative: As the Universe expanded, there became more and more "room" or "opportunity"
for gravitons to escape from our "M brane". It all just simply became larger, and simpler to escape to the bulk.
It's a self-enhancing effect ! Could that then be a consideration? (I don't know)
Note 2: The "vacuum energy density", and "quintessence"
2.1 Introduction.
There are two reasonable candidates for Dark Energy: the (usual) "vacuum energy density" (or cosmological constant),
and something "new" which is called "quintessence".
As a third option, the facinating "Brane Cosmology" should be mentioned. This is the subject of section 3.
Let's first take a look at the first two "candidates".
Some cosmologists describe "quintessence" as a sort of "field that slept, awoke, and now drives the acceleration".
Also, for many cosmologists,"quintessence" is synonymous to "Dark Energy", making both concepts the same thing.
Why can't it just be the "vacuum energy density"? The same cosmologist say that the problem with the cosmological constant,
is, that it is constant, with the same energy density, pressure, and equation of state over time.
The point they make is, that the stuff that's Dark energy, had to be "negligible" at the universe's earliest stages.
If not, the galaxies and all their stars etc.. would never have formed.
That is not a strange idea. If there was a strong negative "pressure" in the beginning, it's really hard
to see how galaxies could have formed.
So, there are advocates who favor the "ordinary" vacuum energy density (or, equivalently, the cosmological constant)
and, on the other hand, advocates who favor "quintessence", which is supposed to be a time-evolving, spatially inhomogeneous
component exerting negative pressure.
2.2 The (ordinary) vacuum energy density
The "cosmological constant" was first introduced by Einstein. His "Theory of General Relativity", implied that
the Universe would collapse, due to gravitational effects.
At that time however, it was believed that the Universe was 'static', so for the purpose of constructing a static model
of the universe, Einstein added the Cosmological Constant. This (repulsive) cosmological constant should then balance
the gravitational attraction of matter. Today, the cosmological constant is by many scientists recognized as vacuum energy,
an energy assigned to empty space itself, that has negative pressure and induces cosmic acceleration (!)
So, the Cosmological Constant really may be associated with negative pressure and accelerated expansion(!)
In my notes, you will not find mutch math. But the following nice example, will demonstrate why the vacuum energy
relates to accelerated expansion "of space", or "the vacuum".
Needless to say that Einsteins General Relativity (GR) equations are pretty tough.
The Friedmann–Lemaître–Robertson–Walker (FLRW) metric is an certain solution of Einstein's field equations of GR.
It uses certain asumptions, like a homogeneous, isotropic Universe. Many scientists regard it to be at least a usable
first order approcimation. Below you see some of the results:
In second equation, if you look at the first term on the right of the "=", actually tells us that both the energy density
and the pressure cause the expansion rate of the universe to decrease, as a consequence of gravitation.
But (!) the second part on the right, thus cosmological constant Λ, on the other hand, causes an acceleration
in the expansion of the universe.
To put it simple: the equation says that the rate of acceleration (a), is a "negative part" plus a "positive part", which is
equivalent to saying "attraction due to gravity" plus "repulsion due to negative pressure of the vacuum".
If the second term is larger than the first term, we then have a positive rate of acceleration (!)
This is why some scientists concentrate on the cosmological constant. But as said before, the fact that it is regarded
as a "constant", does not explain why the repulsion in the very early Universe must have been low, that is, low enough
for galaxies to form.
By the way, not all scientists are really convinced the cosmological constant, was trully constant all the time. But, that's all
quite speculative at this time.
And, some mathematical treatments show that even a constant Λ will give rise to an accelerated Universe, although
it seems difficult to reconcile that with the early formation of galaxies.
It's quite fair to say that we do not have a "very" clear picture right now.
2.3 Quintessence
What is a reasonable description of quintessence ? Is it the same, or part of, the vacuum energy?
In fact, it is not easy to answer the last question.
Some arguments might be the following:
1. the vacuum energy or Cosmological constant, is (supposedly) "constant" in space and time. This is likely not be so
for quintessence. That field should be "low in magitude" at the early stages of the Universe, while at a later phase,
it increased significantly: there must be a period in the early Universe where this force was negligible,
otherwise galaxies and stars would probably not have formed.
This, as many scientists assumes, sets quintessence "apart" from the Cosmological Constant.
2. The vacuum energy, or "vacuum fluctuations", as is understood in small scale observations as for example,
in the "Casimir effect", or the "Lamb" shift in spectral lines of Hydrogen (and other elements), is contributed
to the virtual particles, or quantum fluctuations, in the local vacuum.
This is likely not to be attributed to quintessence.
3. Both the vacuum energy and quintessence, can be expressed by the "equation of state", w ~ p/p' where p
is the pressure and p' is the is the energy density. For the vacuum, w is believed to be "-1".
Different ideas on quintessence, produces a different "w".
What seems to be characteristic for quintessence, is that it's scalar value is often viewed as a "slow rolling potential",
In the equation on the left, the wavelength should be very long, that is, a slow rolling potential with little
kinetic energy and a larger potential part (second term on the leftside of the "=").
Simply put: in the equation above, you see on the right side of the "=", a postive term and a negative term.
Now, if the kinetic energy is smaller (due to the slow roll) than the negative potential term, we have a a negative pressure.
This then, implies an accelerated expansion.
So what's best? Vacuum energy density or quintessence, or still something else? There are advocates for both models.
But if you take a look at the number of publications on quintessence, or quintessence in combination with the
"new" inflationary theory (a renewed theory from Guth's original one), it seems that "quintessence"
is quite popular among scientists.